KMS-symmetric Markov semigroups
type: Item
instance of: scholarly article
title: KMS-symmetric Markov semigroups
zbMATH Open document ID: 0828.47036
DOI: 10.1007/BF02572383
author: Stanisław Goldstein
author: J. Martin Lindsay
published in: Mathematische Zeitschrift
publication date: 1996-01-08T00:00:00Z
full work available at URL: https://eudml.org/doc/174791
review text: Positivity preserving contraction semigroups on a \(W^*\)-algebra which are symmetric with respect to a state on the algebra naturally extend to the Haagerup \(L^p\)-spaces over the algebra. The self-adjoint contraction semigroups on \(L^2\) that arise in this way are characterised by Beurling-Deny type criteria for the corresponding quadratic form generator. Conversely, a closed Dirichlet form on \(L^2\) uniquely determines a KMS-symmetric, positivity preserving contraction semigroup on the algebra. Moreover complete positivity for the semigroup corresponds to the quadratic form being completely Dirichlet in a natural sense. The notion of symmetry employed here is, in general, different from detailed balance as usually defined, and involves the symmetric embedding, rather than the GNS embedding, of the algebra into \(L^2\). The present theory extends earlier results of Albeverio and Høegh- Krohn, and recent work of Davies and Lindsay, on semigroups which are symmetric with respect to a trace.
reviewed by: Stanisław Goldstein
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 795324
zbMATH Keywords: positivity preserving contraction semigroups on a \(W^*\)-algebra
zbMATH Keywords: symmetric with respect to a state
zbMATH Keywords: Haagerup \(L^ p\)-spaces
zbMATH Keywords: self-adjoint contraction semigroups
zbMATH Keywords: Beurling-Deny type criteria
zbMATH Keywords: quadratic form generator
zbMATH Keywords: closed Dirichlet form
zbMATH Keywords: GNS embedding
MaRDI profile type: Publication
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OpenAlex ID: W2056902751
description: scientific article; zbMATH DE number 795324