Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

The C*-algebra of ax+b-like groups

We describe the C*-algebras of " ax+b" -like groups in terms of algebras of operator fields defined over their dual spaces.

The solvable Lie group N_{6, 28}: an example of an almost C_0(\mathcal{K})-C*-algebra

Motivated by the description of the C*-algebra of the affine automorphism group N6,28 of the Siegel upper half-plane of degree 2 as an algebra of operator fields defined over the unitary dual View the MathML source of the group, we introduce a family of C*-algebras, which we call almost C0(K), and we show that the C*-algebra of the group N6,28 belongs to this class.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Tensor products of operator systems

The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular examples of tensor products, including a minimal, maximal, maximal commuting, maximal injective and some asymmetric tensor products. We characterize these tensor products in terms of their universal properties and give descriptions of their positive cones. We also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system. We examine notions of nuclearity for our tensor products which, on the category of C*-algebras, reduce to the classical notion. We exhibit an operator system S which is not completely order isomorphic to a C*-algebra yet has the property that for every C*-algebra A, the minimal and maximal tensor product of S and A are equal.

Domain annihilation due to temperature and thickness gradients in single-crystal BaTiO3

The manner in which 90? ferroelectric-ferroelastic domains respond to changes in temperature has been mapped in BaTiO3 single crystals using atomic force microscopy. Domain periodicity remains unaltered until approximately 2 ? C below the Curie temperature (TC ), whereupon domains coarsened dramatically. This behavior was successfully rationalized by considering the temperature dependence of the parameters associated with standard models of ferroelastic domain formation. However, while successful in describing the expected radical increase in equilibrium period with temperature, the model did not predict the unusual mechanism by which domain coarsening occurred; this was not continuous at a local level but instead involved discrete domain annihilation events. Subsequent insights from a combination of free energy analysis for the system and further experimental data from an analogous situation, in which domain period increases with increasing crystal thickness, suggested that domain annihilation is inevitable whenever a component of the relevant gradient that affects domain period is orientated parallel to the domain walls. Consistent with this thesis, we note that, for the observations presented herein, the thermal gradient possessed a significant component parallel to the domain walls. We suggest that domain annihilation is a general feature of domain structures in gradient fields.

Quotients, exactness, and nuclearity in the operator system category

We continue our study of tensor products in the operator system category. We define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products. One of our main goals is to relate these refinements of nuclearity to the Kirchberg conjecture. In particular, we prove that the Kirchberg conjecture is equivalent to the statement that every operator system that is (min,er)-nuclear is also (el,c)-nuclear. We show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient. We prove that an operator system is exact for the min tensor product if and only if it is (min,el)-nuclear. We give many characterizations of operator systems that are (min,er)-nuclear, (el,c)-nuclear, (min,el)-nuclear and (el,max)-nuclear. These characterizations involve operator system analogues of various properties from the theory of C*-algebras and operator spaces, including the WEP and LLP.

Mapping stone surface temperature fluctuations: Implications for lichen distribution and biomodification on historic stone surfaces

The exposure of historic stone to processes of lichen-induced surface biomodification is determined, first and foremost, by the bioreceptivity of those surfaces to lichen colonization. As an important component of surface bioreceptivity, spatiotemporal variation in stone surface temperature plays a critical role in the spatial distribution of saxicolous lichen on historic stone structures, especially within seasonally hot environments. The ornate limestone and tufa stairwell of the Monastery of Cartuja (1516), Granada, Spain, exhibits significant aspect-related differences in lichen distribution. Lichen coverage and
diurnal fluctuations in stone surface temperature on the stairwell were monitored and mapped, under anticyclonic conditions in summer and winter, using an infrared thermometer and Geographical Information Systems approach. This research suggests that it is not extreme high surface temperatures that
determine the presence or absence of lichen coverage on stonework. Instead, average stone surface temperatures
over the course of the year seem to play a critical role in determining whether or not surfaces are receptive to lichen colonization and subsequent biomodification. It is inferred that lichen, capable of surviving extreme surface temperatures during the Mediterranean summer in an ametabolic state, require a respite period of lower temperatures within which they can metabolize, grow and reproduce.
The higher the average annual temperature a surface experiences, the shorter the respite period for any lichen potentially inhabiting that surface. A critical average temperature threshold of approximately 21 ?C has been identified on the stairwell, with average stone surface temperatures greater than this
generally inhibiting lichen colonization. A brief visual condition assessment between lichen-covered and lichen-free surfaces on the limestone sections of the stairwell suggests relative bioprotection induced by lichen coverage, with stonework quality and sharpness remaining more defined beneath lichen-covered surfaces. The methodology employed in this paper may have further applications in the monitoring and mapping of thermal stress fatigue on historic building materials.

Characterisations of the weak expectation property

We use representations of operator systems as quotients to deduce various characterisations of the weak expectation property (WEP) for C∗ -algebras. By Kirchberg’s work on WEP, these results give new formulations of Connes’ embedding problem.

C∗-Segal algebras with order unit

We introduce the notion of a (noncommutative) C *-Segal algebra as a Banach algebra (A, {norm of matrix}{dot operator}{norm of matrix} A) which is a dense ideal in a C *-algebra (C, {norm of matrix}{dot operator}{norm of matrix} C), where {norm of matrix}{dot operator}{norm of matrix} A is strictly stronger than {norm of matrix}{dot operator}{norm of matrix} C onA. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of C *-Segal algebras with order unit is determined.

An electrochemical study of PCl3 and POCl3 in the room temperature ionic liquid [C(4)mpyrr][N(Tf)(2)]

Voltammetric studies of PCl3 and POCl3 have not been reported in the literature to date, probably due to the instability of these molecules in conventional aprotic solvents giving unstable and irreproducible results. From a previous study [Amigues et al. Chem. Commun. 2005, 1-4], it was found that ionic liquids have the ability to offer a uniquely stable solution phase environment for the study of these phosphorus compounds. Consequently, the electrochemistry of PCl3 and POCl3 has been studied by cyclic voltammetry on a gold microelectrode in the ionic liquid [C(4)mpyrr][N(Tf)(2)] (1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl) imide). For both compounds, reduction and oxidation waves were observed and a tentative assignment of the waves is given. For PCl3, the reduction was thought to proceed via the following mechanism: PCl3 + e(-) h reversible arrow PCl3-, PCl3- reversible arrow Cl- + (PCl2)-Cl-center dot, (and) Cl- + PCl3 h PCl4-. For POCl3, the suggested reduction mechanism was analogous to that of PCl3: POCl3 + e(-) reversible arrow POCl3-, POCl3- reversible arrow Cl- + (POCl2)-O-center dot, and Cl- + POCl3 h POCl4-. In both cases (PCl2)-Cl-center dot and (POCl2)-O-center dot are likely to engage in further reactions. Potential step microdisk chronoamperometry was carried out on the reductive waves of PCl3 and POCl3 to measure diffusion coefficients and number of electrons transferred. It was found that the diffusion of PCl3 was unusually slow (3.1 x 10(-12) m(2) s(-1)): approximately 1 order of magnitude less than that for POCl3 (2.2 x 10(-11) m(2) s(-1)). For both PCl3 and POCl3, a