scientific article
From MaRDI portal
zbMath0699.46048MaRDI QIDQ3477514
Eizaburo Kamei, Jun Ichi Fujii
Publication date: 1989
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hilbert spaceRelative entropies for positive linear forms on operator algebrasrelative operator entropy for bounded positive operators on arelative operator entropy for bounded positive operators on a Hilbert space
Free probability and free operator algebras (46L54) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Functional calculus for linear operators (47A60) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Measures of information, entropy (94A17)
Related Items
The quantum ♮α-Rényi divergence of real order, A survey on operator monotonicity, operator convexity, and operator means, Functional version for Furuta parametric relative operator entropy, Relative entropy and Tsallis entropy of two accretive operators, Further inequalities involving the weighted geometric operator mean and the Heinz operator mean, Log-majorization Type Inequalities, Ando-Hiai Inequality: Extensions and Applications, Relative Operator Entropy, Equivalence relations among inequalities for some relative operator entropies, Two-variable Wasserstein means of positive definite operators, Quantum Fokker-Planck dynamics, Upper and lower bounds for noncommutative perspectives of operator monotone functions: the case of second variable, Further generalizations of Bebiano-Lemos-Providência inequality, ON SOME TSALLIS RELATIVE OPERATOR ENTROPY PROPERTIES RELATED TO HELLINGER METRICS, Relative operator entropies and Tsallis relative operator entropies in JB-algebras, Lipschitz type inequalities for noncommutative perspectives of operator monotone functions in Hilbert spaces, On time-reversal and space-time harmonic processes for Markovian quantum channels, The \(n\)-th relative operator entropies and the \(n\)-th operator divergences, Bounds of some relative operator entropies in a general form, Path of quasi-means as a geodesic, FUNCTIONAL VERSIONS OF SOME REFINED AND REVERSED OPERATOR MEAN INEQUALITIES, Some bounds for the generalized Tsallis relative operator entropy, On a new generalized Tsallis relative operator entropy, Operator inequalities related to Young's inequality, Operator valued inequalities based on Young's inequality, Optimal Self-Concordant Barriers for Quantum Relative Entropies, A complementary inequality for the information monotonicity of the operator perspective and applications, Refined estimations for some types of entropies and divergences, Operator entropy and fidelity associated with the geometric mean, Unnamed Item, CONVEXITY OF PARAMETER EXTENSIONS OF SOME RELATIVE OPERATOR ENTROPIES WITH A PERSPECTIVE APPROACH, Operator inequalities associated with \(A\log A\) via Specht ratio., Choi-Davis-Jensen's inequality without convexity, Unnamed Item, Unnamed Item, The \(n\)-th residual relative operator entropy \({\mathfrak{R}}^{[n}_{x,y}(A|B)\)], Quantum f-divergences in von Neumann algebras. II. Maximal f-divergences, OPERATOR QUASILINEARITY OF SOME FUNCTIONALS ASSOCIATED WITH DAVIS–CHOI–JENSEN’S INEQUALITY FOR POSITIVE MAPS, On operator inequalities of some relative operator entropies, Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators., Matrix trace inequalities on Tsallis relative entropy of negative order, Geometric interpolation in symmetrically-normed ideals, Some extensions of the operator entropy type inequalities, The unique solution of the Karcher equation and the self-adjointness of the Karcher mean, The proper formula for relative entropy and its asymptotics in quantum probability, Bregman divergence as relative operator entropy, Relative operator entropy related with the spectral geometric mean, Semidefinite approximations of the matrix logarithm, Unnamed Item, Some inequalities involving quadratic forms of operator means, Inequalities for relative operator entropies and operator means, Matrix trace inequalities related to the Tsallis relative entropies of real order, A difference counterpart to a matrix Hölder inequality, The relative operator entropy and the Karcher mean, Reverse inequalities involving two relative operator entropies and two relative entropies, The Golden-Thompson trace inequality is complemented, Convergence of logarithmic trace inequalities via generalized Lie--Trotter formulae, Trace inequalities for logarithms and powers of J-Hermitian matrices, New refinements of some inequalities involving relative operator entropy, Generalized Shannon inequalities based on Tsallis relative operator entropy, On trace inequalities and their applications to noncommutative communication theory, Inequalities for quantum relative entropy, Precise evaluation of leaked information with secure randomness extraction in the presence of quantum attacker, Some remarks on Tsallis relative operator entropy, Improved operator inequalities of some relative operative entropies, Inequalities for relative operator entropy in terms of Tsallis’ entropy, Refining and reversing the weighted arithmetic-geometric mean inequality involving convex functionals and application for the functional entropy, Pusz-Woronowicz functional calculus and extended operator convex perspectives, Sharp bounds for the Tsallis relative operator entropy, Some trace inequalities for exponential and logarithmic functions, Means for fixed rank PSD matrices, Structure of Hiai-Petz parametrized geometry for positive definite matrices, A note on operator inequalities of Tsallis relative operator entropy, Some estimations for the generalized relative operator entropy, Two reverse inequalities associated with Tsallis relative operator entropy via generalized Kantorovich constant and their applications, Revisiting the Grüss inequality, Inequalities for the generalized Tsallis relative operator entropy, Shannon like inequalities for \(f\)-connections of positive linear maps and positive operators, Refined operator inequalities for relative operator entropies, More results on weighted means
