Quasi-entropies for states of a von Neumann algebra
type: Item
instance of: scholarly article
title: Quasi-entropies for states of a von Neumann algebra
zbMATH Open document ID: 0606.46039
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1985-01-01T00:00:00Z
review text: The relative entropy functional of Araki is generalized. Let M be a von Neumann algebra with normal states \(\phi\) and \(\omega\). Our quasi-entropy \(S^ k_ f(\phi,\omega)\) depends on two parameters \(k\in M\) and f: [0,\(\infty)\to {\mathbb{R}}\). The counterpart of the quasi-entropy in classical information theory is the f-divergence of Csiszár. In the paper Lieb's concavity is recaptured in Kosaki's form. Continuity and monotonity theorems are discussed. The main technique is the application of the theory of operator monotone functions.
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 81Q99
zbMATH DE Number: 3979789
zbMATH Keywords: Jensen's inequality
zbMATH Keywords: relative modular operator
zbMATH Keywords: operator convex function
zbMATH Keywords: relative entropy functional of Araki
zbMATH Keywords: normal states
zbMATH Keywords: quasi-entropy
zbMATH Keywords: f- divergence of Csiszár
zbMATH Keywords: Continuity
zbMATH Keywords: operator monotone functions
author: Dénes Petz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195178929
OpenAlex ID: W2007159481
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DOI: 10.2977/PRIMS/1195178929
description: scientific article; zbMATH DE number 3979789