Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Methodische Entwicklung der MALDI-TOF-Massenspektrometrie für Grenzbereiche der Polymeranalytik

Zusammenfassung der DoktorarbeitDie MALDI-TOF-Massenspektrometrie (Matrix Assisted Laser Desorption and Ionisation–Time Of Flight) ist in der Lage, Moleküle mit einem Molekulargewicht bis zu mehreren Hunderttausend Da intakt in die Gasphase zu überführen. Dabei wird die Fragmentierung des Analyten stark eingeschränkt bzw. gänzlich vermieden. Diese Methode findet daher zunehmend Verwendung für die Charakterisierung von Biopolymeren und synthetischen Polymeren. Ziel dieser Arbeit war, die MALDI-TOF-Massenspektrometrie zur Charakterisierung von Makromolekülen einzusetzen, bei denen die konventionellen polymeranalytischen Methoden nur unzureichende Informationen oder gar falsche bzw. gar keine Ergebnisse liefern. Mittels einer methodischen Entwicklung der MALDI-TOF-Massenspektrometrie gelang es, die bisherigen Grenzen der Methode zu erweitern und neue Anwendungsbereiche der Polymeranalytik aufzuzeigen. Anhand der erzielten Ergebnisse wurden darüber hinaus neue Erklärungsansätze formuliert, die zu einem besseren Verständnis des noch immer ungeklärten MALDI-Prozesses beitragen können. Besonders vielversprechend sind zum einen die Ergebnisse der Fragmentionenanalyse synthetischer Polymere und zum anderen die Charakterisierung von unlöslichen PAHs (Polycyclic Aromatic Hydrocarbons). Die Möglichkeiten und Aussagekraft der Fragmentionenanalyse wurde an synthetischen Polymeren getestet. Mit Hilfe dieser neuen Technik konnte die komplizierte Endgruppenverteilung einer Polycarbonat-Probe sowie die Zusammensetzung eines Poly-para-phenylenethynylen-b-Polyethylenoxid-Diblock-Copolymers eindeutig bestimmen werden, während die konventionellen MALDI-Massenspektren nur über einen wesentlich geringeren Informationsgehalt verfügten. Auf dem Gebiet der Analytik von unlöslichen PAHs wurde mit der Entwicklung einer neuen MALDI-Probenvorbereitung eine Methode gefunden, die über die PAH Analytik hinaus von großem Nutzen ist. Diese erstmalig angewendete Probenvorbereitung unterscheidet sich von den üblichen MALDI-Probenpräparationen, indem sie auf die Beteiligung eines Lösungsmittels vollkommen verzichtet. Damit konnte speziell ein unlöslicher, zuvor nicht nachweisbarer PAH von ca. 2700 Da mit MALDI eindeutig charakterisiert werden.

Ectomycorrhizae of sessile oak (Quercus petraea (Matt.) Liebl.)

Investigations were performed during the years 1999 to 2001 on a limed and unlimed plot within a high-elevated sessile oak forest. The oak forest (with 90 years old European beech at the understorey) was 170 to 197 years old. It is located at forest district Merzalben, location 04/0705, which is situated in the Palatinate Forest in south-west Germany. Liming was performed in December 1988 when 6 tons/ha of powdered Dolomite were brought up by the forestry department. Liming was performed to counteract the effects of soil acidification (pH(H2O) at Horizon A (0-10 cm): 3.9), which is induced by long-term (anthropogenic) acidic cloud cover and precipitation. Potentially toxic Al3+ ions, which become solubilized below pH 5, were suspected to be responsible for forest dieback and sudden death of the mature oaks. The most logical entry point for these toxic ions was suspected to occur in the highly absorptive region of the ectomycorrhizae (fungal covered root tips). However, the diversity and abundance of oak-ectomycorrhizal species and their actual roles in aluminum translocation (or blockage) were unknown. It was hypothesized that the ectomycorrhizae of sessile oaks in a limed forest would exhibit greater seasonal diversity and abundance with less evidence of incorporated aluminum than similar oak ectomycorrhizae from unlimed soils. To test this hypothesis, 12 oaks in the limed plot and 12 in an adjacent unlimed plot were selected. Each spring and fall for 2 years (1999 & 2000), 2 sets of soil cylinders (9.9 cm dia.) were extracted from Horizon A (0-10 cm), Horizon B (30-40 cm) and Horizon C (50-60 cm depth) at a distance of 1 meter from each tree base. Roots were extracted from each probe by gentle sieving and rinsing. Soil samples were retained for pH (H2O, CaCl2, and KCl) and moisture analysis. One set of roots was sorted by size and air-dried for biomass analysis. The finest mycorrhizal roots of this set were used for bound and unbound (cytosolic) mineral [Al, Ca, Mg, K, Na, Mn, S, Zn, Fe, Cd and Pb] analysis (by Landwirtschaftliche Untersuchungs- und Forschungsanstalt Rheinland Palatinate (LUFA)). Within 7 days of collection, the mycorrhizal tips from the second set of probes were excised, sorted, identified (using Agerer’s Color Atlas), counted and weighed. Seasonal diversity and abundance was characterized for 50 of the 93 isolates. The location and relative abundance of Al within the fungal and root cell walls was characterized for 68 species using 0.01% Morin dye and fluorescence microscopy. Morin complexes with Al to produce an intense yellow fluorescence. The 4 most common species (Cenococcum geophilum, Quercirhiza fibulocsytidiata, Lactarius subdulcis, Piceirhiza chordata) were prepared for bound Al, Ca, Fe and K mineral analysis by LUFA. The unlimed and limed plots were then compared. Only 46 of the 93 isolated ectomycorrhizal species had been previously associated with oaks in the literature. Mycorrhizal biomass was most abundant in Horizon A, declining with depth, drought and progressive soil acidification. Mycorrhizae were most diverse (32 species) in the limed plot, but individual species abundance was low (R Selection) in comparison to the unlimed plot, where there were fewer species (24) but each species present was abundant (K Selection). Liming increased diversity and altered dominance hierarchy, seasonal distributions and succession trends of ectomycorrhizae at all depths. Despite an expected reduction in Al content, the limed ectomycorrhizae both qualitatively (fluorescence analysis) and quantitatively (mineral analysis) contained more bound Al, especially so in Horizon A. The Al content qualitatively and quantitatively increased with depth in the unlimed and limed plots. The bound Al content fluctuated between 4000-and 20000 ppm while the unbound component was consistently lower (4 -14 ppm). The relative amount of unbound Al declined upon liming implying less availability for translocation to the crown area of the trees. This correspouds with the findings of good crown appearance and lower tree mortality in the limed zone. Each ectomycorrhizal species was unique in its ability to block, sequester (hold) or translocate Aluminum. In several species, Al uptake varied with changes in moisture, pH, depth and liming. According to the fluorescence study, about 48% of the isolated ectomycorrhizal species blocked and/or sequestered (held) Al in their mantle and/or Hartig net walls, qualitatively lowering bound Al in the adjacent root cell walls. Generally, if Al was more concentrated in the fungal walls, it was less evident in the cortex and xylem and conversely, if Al was low or absent from the fungal walls it was frequently more evident in the cortex and xylem.

Algebraische Beschreibung von Symmetrien: das Modell der Nichtkommutativen Multi-Tori

In der Nichtkommutativen Geometrie werden Räume und Strukturen durch Algebren beschrieben. Insbesondere werden hierbei klassische Symmetrien durch Hopf-Algebren und Quantengruppen ausgedrückt bzw. verallgemeinert. Wir zeigen in dieser Arbeit, daß der bekannte Quantendoppeltorus, der die Summe aus einem kommutativen und einem nichtkommutativen 2-Torus ist, nur den Spezialfall einer allgemeineren Konstruktion darstellt, die der Summe aus einem kommutativen und mehreren nichtkommutativen n-Tori eine Hopf-Algebren-Struktur zuordnet. Diese Konstruktion führt zur Definition der Nichtkommutativen Multi-Tori. Die Duale dieser Multi-Tori ist eine Kreuzproduktalgebra, die als Quantisierung von Gruppenorbits interpretiert werden kann. Für den Fall von Wurzeln der Eins erhält man wichtige Klassen von endlich-dimensionalen Kac-Algebren, insbesondere die 8-dim. Kac-Paljutkin-Algebra. Ebenfalls für Wurzeln der Eins kann man die Nichtkommutativen Multi-Tori als Hopf-Galois-Erweiterungen des kommutativen Torus interpretieren, wobei die Rolle der typischen Faser von einer endlich-dimensionalen Hopf-Algebra gespielt wird. Der Nichtkommutative 2-Torus besitzt bekanntlich eine u(1)xu(1)-Symmetrie. Wir zeigen, daß er eine größere Quantengruppen-Symmetrie besitzt, die allerdings nicht auf die Spektralen Tripel des Nichtkommutativen Torus fortgesetzt werden kann.

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Climate signatures in corals of the tropical-temperate transition zone (Late Miocene, Crete/Greece)

The present study describes a Late Miocene (early Tortonian - early Messinian) transitional carbonate system that combines elements of tropical and cool-water carbonate systems (Irakleion Basin, island of Crete, Greece). As documented by stratal geometries, the submarine topography of the basin was controlled by tilting blocks. Coral reefs formed by Porites and Tarbellastrea occurred in a narrow clastic coastal belt along a „central Cretan landmass“, and steep escarpments formed by faulting. Extensive covers of level-bottom communities existed in a low-energy environment on the gentle dip-slope ramps of the blocks that show the widest geographical distribution within the basin. Consistent patterns of landward and basinward shift of coastal onlap in all outcrop studies reveal an overriding control of 3rd and 4th order sea level changes on sediment dynamics and facies distributions over block movements. An increasingly dry climate and the complex submarine topography of the fault block mosaic kept sediment and nutrient discharge at a minimum. The skeletal limestone facies therefore reflects oligotrophic conditions and a sea surface temperature (SST) near the lower threshold temperature of coral reefs in a climatic position transitional between the tropical coral reef belt and the temperate zone. Stable isotope records (δ18O, δ13C) from massiv, exceptionally preserved Late Miocene aragonite coral skeletons reflect seasonal changes in sea surface temperature and symbiont autotrophy. Spectral analysis of a 69 years coral δ18O record reveals significant variance at interannual time scales (5-6 years) that matches the present-day eastern Mediterranean climate variability controlled by the Arctic Oscillation/North Atlantic Oscillation (AO/NAO), the Northern Hemisphere’s dominant mode of atmospheric variability. Supported by simulations with a complex atmospheric general circulation model coupled to a mixed-layer ocean model, it is suggested, that climate dynamics in the eastern Mediterranean and central Europe reflect atmospheric variability related to the Icelandic Low 10 million years ago. Usually, Miocene corals are transformed in calcite spar in geological time and isotope values are reset by diagenetic alteration. It is demonstrated that the relicts of growth bands represent an intriguing source of information for the growth conditions of fossil corals. Recrystallized growth bands were measured systematically in massive Porites from Crete. The Late Miocene corals were growing slowly with 2-4 mm/yr, compatible with present-day Porites from high latitude reefs, a relationship that fits the position of Crete at the margin of the Miocene tropical reef belt. Over Late Miocene time (Tortonian - early Messinian) growth rates remained remarkably constant, and if the modern growth temperature relationship for massive Porites applies to the Neogene, minimum (winter) SST did not exceed 19-21°C.

Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

Entwicklung einer Kryokonservierungsmethode für Spermien der Honigbiene, Apis mellifera

Die westliche Honigbiene (Apis mellifera) ist von großer ökologischer und ökonomischer Bedeutung. Seit Jahren zeichnen sich in Nordamerika sowie in manchen Teilen Europas rückläufige Bienenvölkerzahlen und eine abnehmende Artenvielfalt innerhalb der Bienenfamilie ab. Mittlerweile ist von einer globalen Bestäuberkrise die Rede und es wird verstärkt nach Möglichkeiten gesucht, um dieser Krise entgegenzuwirken. Eine Konservierung von Bienenspermien in flüssigem Stickstoff ohne Fruchtbarkeitsreduzierung würde die Bienenzucht revolutionieren und stark beschleunigen, da räumliche und zeitliche Restriktionen bei der Wahl des Bienenspermas wegfielen. Zudem wäre eine Möglichkeit zur Sicherung der genetischen Diversität geschaffen. Im Rahmen des hier vorgestellten Projektes wurde eine solche Methode erarbeitet. In umfangreichen Abkühl- und Einfrierversuchen konnte eine neue Konservierungstechnik entwickelt werden, bei der das Kryoprotektivum mittels Dialyse dem Bienensperma zugesetzt wird. Dieses Verfahren erhält die native Spermaform, in der die Spermien parallel und inaktiv in dicht gepackten Clustern vorliegen, und erzielt bisher unerreichte Besamungserfolge. So konnten durchschnittlich 1,25 Mio. Spermien in den Spermatheken besamter Königinnen gezählt werden und davon waren ungefähr 90% motil. Besonders vielversprechend ist jedoch, dass 79,4% der Brut weiblich waren. Ein so hoher Anteil weiblicher Brut konnte bislang nicht erreicht werden und wäre für züchterische Zwecke ausreichend.