Let A be a C *-algebra, T be a locally compact Hausdorff space equipped with a probability measure P and let (A t) t∈T be a continuous field of operators in A such that the function t → A t is norm continuous on T and the function t → A t is integrable. Then the following equality including Bouchner integrals holds T A t − T A s dP 2 dP = T |A t | 2 dP − T A t dP 2. (0.1) This equality is relat...

This article provides sufficient conditions for positive maps on the Schatten classes Jp; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1, the space of trace class operators, to have a unique, stric...

We prove new results about the robustness of well-known convex noise-blind optimization formulations for reconstruction low-rank matrices from an underdetermined system random linear measurements. Specifically, our address Hermitian rank-one measurements as used in a version phase retrieval problem; that is, each measurement can be represented inner product unknown matrix and outer given realiz...

Perturbations (r τt)t≥0 of the semigroup of shifts (τt)t≥0 on L(R+) are studied under the assumption that r τt−τt belongs to a certain Schatten–von Neumann class Sp with p ≥ 1. It is shown that, for the unitary component in the Wold– Kolmogorov decomposition of the cogenerator of the semigroup (r τt)t≥0, any singular spectral type may be achieved by S1-perturbations. An explicit construction is...

We give estimates for the approximation numbers of composition operators on H, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approximation numbers are dominated by e−c √ . When the symbol is continuous on the closed unit disk and has a domain touching the boundary non-tangentially at a finite number of points, with a good behavior a...

We study the decay of approximation numbers of compact composition operators on the Dirichlet space. We give upper and lower bounds for these numbers. In particular, we improve on a result of O. El-Fallah, K. Kellay, M. Shabankhah and A. Youssfi, on the set of contact points with the unit circle of a compact symbolic composition operator acting on the Dirichlet space D. We extend their results ...