Operator entropy inequalities

• Autorzy: M. S. Moslehian , F. Mirzapour , A. Morassaei
• Języki publikacji: EN

Abstrakty

EN

We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A = (A₁,...,Aₙ) and B = (B₁,...,Bₙ) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting
$S_q^f(A|B): = ∑_{j=1}^{n} A_j^{1/2} (A_j^{-1/2}B_jA_j^{-1/2})^{q} f(A_j^{-1/2}B_jA_j^{-1/2})A_j^{1/2}$,
and then give upper and lower bounds for $S_q^f(A|B)$ as an extension of an inequality due to T. Furuta [Linear Algebra Appl. 381 (2004), 219-235] under certain conditions. As an application, some inequalities concerning the classical Shannon entropy are deduced.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 46L05: General theory of C * -algebras
• 15A42: Inequalities involving eigenvalues and eigenvectors
• 47A63: Operator inequalities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 130
• Numer: 2
• Strony: 159-168

Daty

wydano

2013

Twórcy

autor

M. S. Moslehian

• Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran

autor

F. Mirzapour

• Department of Mathematics, Faculty of Sciences, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran

autor

A. Morassaei

• Department of Mathematics, Faculty of Sciences, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran

Identyfikatory

DOI

10.4064/cm130-2-2