On certain properties of the relative entropy of states of operator algebras
type: Item
instance of: scholarly article
title: On certain properties of the relative entropy of states of operator algebras
zbMATH Open document ID: 0707.46043
DOI: 10.1007/BF02571350
published in: Mathematische Zeitschrift
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/174232
review text: Several properties of the relative entropy S(\(\phi\),\(\omega\)) of the states \(\phi\) and \(\omega\) of a \(C^*\)-algebra are established. It is proven that \(S(\phi,\omega)=S(\phi | {\mathcal A}_ 1,\omega | {\mathcal A}_ 1)| S(\omega \circ E,\omega)\) if \({\mathcal A}_ 1\), \({\mathcal A}\) are \(C^*\)-algebras and E is a \(\phi\)-preserving conditional expectation onto \({\mathcal A}_ 1\). A fairly general version of the strong superadditivity is obtained and used to prove the existence of the mean relative entropy for an abstract noncommutative stationary Markov chain.
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 1001
zbMATH Keywords: states
zbMATH Keywords: \(C^ *\)-algebra
zbMATH Keywords: conditional expectation
zbMATH Keywords: strong superadditivity
zbMATH Keywords: existence of the mean relative entropy for an abstract noncommutative stationary Markov chain
author: Dénes Petz
reviewed by: Dénes Petz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1001