Related papers: Schutt's theorem for vector-valued sequence spaces

The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction…

Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta \cite{Fu:par} are extended in terms of the parameter of the Tsallis…

We analyse the strong connections between spaces of vector-valued Lipschitz functions and spaces of linear continuous operators. We apply these links to study duality, Schur properties and norm attainment in the former class of spaces as…

Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings…

In this article we continue to study the concept of entropy introduced in [4], [15]-[17]. We calculate entropy for a wider class of finite-dimensional operators in comparison with [15]. We also approximate the entropy of a unitary operator…

The sequence of entropy numbers quantifies the degree of compactness of a linear operator acting between quasi-Banach spaces. We determine the asymptotic behavior of entropy numbers in the case of natural embeddings between…

We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…

We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…

This paper provides some first steps in developing empirical process theory for functions taking values in a vector space. Our main results provide bounds on the entropy of classes of smooth functions taking values in a Hilbert space, by…

We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with a finite spectrum. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to…

We show how the entropy operators for two subsystems may be calculated. In the case of the atom-field interaction we obtain the associated Wigner function for the entropy operator for the quantized field.

We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a…

The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…

We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…

We investigate the hypercube networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information each part of a network shares with the rest of the…

It has been proposed that a quantum group structure underlies de Sitter/Conformal field theory duality. These ideas are used to give a microscopic operator counting interpretation for the entropy of two-dimensional dilaton de Sitter space.…

Schmidt's subspace theorem in terms of Seshadri constants for closed subschemes in subgeneral position has been already developed sharply. We derive our theorem for numerically equivalent ample divisors by dint of the above theory step by…