Mathematische Nachrichten, ( ISI ), Volume (286), No (15), Year (2013-6) , Pages (1514-1529)

Title : ( Non-commutative f-divergence functional )

Authors: Mohammad Sal Moslehian , Mohsen Kian ,

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Abstract

We introduce the non-commutative f -divergence functional Theta( widetilde{A}, widetilde{B}):= int_TB_t^{ frac{1}{2}}f left(B_t^{- frac{1}{2}} A_tB_t^{- frac{1}{2}} right)B_t^{ frac{1}{2}}d mu(t) for an operator convex function f , where widetilde{A}=(A_t)_{t in T} and widetilde{B}=(B_t)_{t in T} are continuous fields of Hilbert space operators and study its properties. We establish some relations between the perspective of an operator convex function $f$ and the non-commutative f -divergence functional. In particular, an operator extension of Csisz {a}r s result regarding f -divergence functional is presented. As some applications, we establish a refinement of the Choi--Davis--Jensen operator inequality, obtain some unitarily invariant norm inequalities and give some results related to the Kullback--Leibler distance.

Keywords

, Information theory; Kullback, , Leibler distance; f, divergence functional; Csisz {a}r s result; perspective function; operator convex
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@article{paperid:1037797,
author = {Sal Moslehian, Mohammad and Kian, Mohsen},
title = {Non-commutative f-divergence functional},
journal = {Mathematische Nachrichten},
year = {2013},
volume = {286},
number = {15},
month = {June},
issn = {0025-584X},
pages = {1514--1529},
numpages = {15},
keywords = {Information theory; Kullback--Leibler distance; f-divergence functional; Csisz {a}r s result; perspective function; operator convex},
}

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%0 Journal Article
%T Non-commutative f-divergence functional
%A Sal Moslehian, Mohammad
%A Kian, Mohsen
%J Mathematische Nachrichten
%@ 0025-584X
%D 2013

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