Relative entropy of states of von Neumann algebras
type: Item
instance of: scholarly article
title: Relative entropy of states of von Neumann algebras
zbMATH Open document ID: 0326.46031
author: Huzihiro Araki
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1976-01-01T00:00:00Z
review text: Relative entropy \(S(\varphi/\psi)\) of two faithful normal positive linear functionals \(\varphi\) and \(\psi\) of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy under restriction to subalgebras are proved. The Wigner-Yanase-Dyson-Lieb concavity is also proved in the context of von Neumann algebras. The definition and the results about relative entropy has been since extended to non-faithful \(\varphi\) and \(\psi\) as well as to the case of \(C^*\)-algebras.
reviewed by: Huzihiro Araki
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 3511002
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195191148
OpenAlex ID: W4239588355
cites work: Tomita's theory of modular Hilbert algebras and its applications
DOI: 10.2977/PRIMS/1195191148
description: scientific article; zbMATH DE number 3511002