Classification and decomposition of quantum Markov semigroups
type: Item
instance of: scholarly article
title: Classification and decomposition of quantum Markov semigroups
zbMATH Open document ID: 1130.46039
author: Veronica Umanità
publication date: 2006-03-21T00:00:00Z
review text: The notions of transience and recurrence play an essential role in the study of Markov processes and in probabilistic potential theory. In [\textit{F.\,Fagnola} and \textit{R.\,Rebolledo}, Probab.\ Theory Relat.\ Fields 126, No.\,~2, 289--306 (2003; Zbl 1024.60031)], transience and recurrence were defined for quantum Markov semigroups and a dichotomy was shown for irreducible semigroups. In the present paper, the transient, fast recurrent, and slow recurrent projections for quantum Markov semigroups on \(\sigma\)-finite von Neumann algebras are defined and their properties are studied. It is shown that they can be used to decompose quantum Markov semigroups as sums of ``sub''-semigroups.
reviewed by: Uwe Franz
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 81S25
zbMATH DE Number: 5014055
zbMATH Keywords: quantum Markov processes
zbMATH Keywords: quantum dynamical semigroups
zbMATH Keywords: recurrence and transience
MaRDI profile type: Publication
full work available at URL: s00440-005-0450-7
OpenAlex ID: W1975367374
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DOI: 10.1007/S00440-005-0450-7
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 5014055