Nature of quantum measurement for quantities not represented by Hermitian operators

In the case of a simple quantum system, we investigate the possibility of defining meaningful probabilities for a quantity that cannot be represented by a Hermitian operator. We find that the consistent-histories approach, recently applied to the case of quantum traversal time [N. Yamada, Phys. Rev. Lett. 83, 3350 (1999)], does not provide a suitable criterion and we dispute Yamada's claim of finding a simple solution to the tunneling-time problem. Rather, we define the probabilities for certain types of generally nonorthogonal decomposition of the system's quantum state. These relate to the interaction between the system and its environment, can be observed in a generalized von Neumann measurement, and are consistent with a particular class of positive-operator-valued measures.

Non-weakly supercyclic operators

Several methods based on an easy geometric argument are provided to prove that a given operator is not weakly supercyclic. The methods apply to different kinds of operators like composition operators or bilateral weighted shifts. In particular, it is shown that the classical Volterra operator is not weakly supercyclic on any of the LP [0, 1] spaces, 1

Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

Time operators for one parameter semigroups

We develop two simple approaches to the construction of time operators for semigroups of continuous linear operators in Hilbert spaces provided that the generators of these semigroups are normal operators. The first approach enables us to give explicit formulas (in the spectral representations) both for the time operators and for their eigenfunctions. The other approach provides no explicit formula. However, it enables us to find necessary and sufficient conditions for the existence of time operators for semigroups of continuous linear operators in separable Hilbert spaces with normal generators. Time superoperators corresponding to unitary groups are also discussed.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

On linear extension operators

We construct a countable-dimensional Hausdorff locally convex topological vector space $E$ and a stratifiable closed linear subspace $F$ subset of $E$ such that any linear extension operator from $C_b(F)$ to $C_b(E)$ is unbounded (here $C_b(X)$ stands for the Banach space of continuous bounded real-valued functions on $X$).

Structure of spectra of linear operators in Banach spaces

Descriptive characterizations of the point, the continuous, and the residual spectra of operators in Banach spaces are put forward. In particular, necessary and sufficient conditions for three disjoint subsets of the complex plane to be the point spectrum, the continuous spectrum, and the residual spectrum of a linear continuous operator in a separable Banach space are obtained.

Amenability of algebras of approximable operators

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson’s space.

Contribution of 30 Biomarkers to 10-year cardiovascular risk estimation in 2 population cohorts: The MONICA, risk, genetics, archiving and monograph (MORGAM) biomarker project

Background— Cardiovascular risk estimation by novel biomarkers needs assessment in disease-free population cohorts, followed up for incident cardiovascular events, assaying the serum and plasma archived at baseline. We report results from 2 cohorts in such a continuing study.
Methods and Results— Thirty novel biomarkers from different pathophysiological pathways were evaluated in 7915 men and women of the FINRISK97 population cohort with 538 incident cardiovascular events at 10 years (fatal or nonfatal coronary or stroke events), from which a biomarker score was developed and then validated in the 2551 men of the Belfast Prospective Epidemiological Study of Myocardial Infarction (PRIME) cohort (260 events). No single biomarker consistently improved risk estimation in FINRISK97 men and FINRISK97 women and the Belfast PRIME Men cohort after allowing for confounding factors; however, the strongest associations (with hazard ratio per SD in FINRISK97 men) were found for N-terminal pro-brain natriuretic peptide (1.23), C-reactive protein (1.23), B-type natriuretic peptide (1.19), and sensitive troponin I (1.18). A biomarker score was developed from the FINRISK97 cohort with the use of regression coefficients and lasso methods, with selection of troponin I, C-reactive protein, and N-terminal pro-brain natriuretic peptide. Adding this score to a conventional risk factor model in the Belfast PRIME Men cohort validated it by improved c-statistics (P=0.004) and integrated discrimination (P<0.0001) and led to significant reclassification of individuals into risk categories (P=0.0008).
Conclusions— The addition of a biomarker score including N-terminal pro-brain natriuretic peptide, C-reactive protein, and sensitive troponin I to a conventional risk model improved 10-year risk estimation for cardiovascular events in 2 middle-aged European populations. Further validation is needed in other populations and age groups.

Kassorins: Novel innate immune system peptides from skin secretions of the African hyperoliid frogs, Kassina maculata and Kassina senegalensis

From defensive skin secretions acquired from two species of African hyperoliid frogs, Kassina maculata and Kassina senegalensis, we have isolated two structurally related, C-terminally amidated tridecapeptides of novel primary structure that exhibit a broad spectrum of biological activity. In reflection of their structural novelty and species of origin, we named the peptides kassorin M (FLEGLLNTVTGLLamide; 1387.8 Da) and kassorin S (FLGGILNTITGLLamide; 1329.8 Da), respectively. The primary structure and organisation of the biosynthetic precursors of kassorins M and S were deduced from cloned skin secretion-derived cDNA. Both open-reading frames encoded a single copy of kassorin M and S, respectively, located at the C-terminus. Kassorins display limited structural similarities to vespid chemotactic peptides (7/13 residues), temporin A (5/13 residues), the N-terminus of Lv-ranaspumin, a foam nest surfactant protein of the frog, Leptodactylus vastus, and an N-terminal domain of the equine sweat surfactant protein, latherin. Both peptides elicit histamine release from rat peritoneal mast cells. However, while kassorin S was found to possess antibacterial activity against Staphylococcus aureus, kassorin M was devoid of such activity. In contrast, kassorin M was found to contract the smooth muscle of guinea pig urinary bladder (EC50 = 4.66 nM) and kassorin S was devoid of this activity. Kassorins thus represent the prototypes of a novel family of peptides from the amphibian innate immune system as occurring in defensive skin secretions.

On the spectrum of frequently hypercyclic operators

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.