Entropy for a Pair of Subalgebras via Automorphisms

This is an expository survey article based on a talk for the Special Session (Operator Algebra) in AMC 2009. For two subalgebras A and B of a finite von Neumann algebra M, we discuss a modified version h(A|B) of the Connes-St rømer relative entropy H(A|B). As one of the most elementary examples, we...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 33; no. 3
Main Author Choda, Marie
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.01.2010
Subjects
Mathematics
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ISSN0126-6705
2180-4206

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Summary:This is an expository survey article based on a talk for the Special Session (Operator Algebra) in AMC 2009. For two subalgebras A and B of a finite von Neumann algebra M, we discuss a modified version h(A|B) of the Connes-St rømer relative entropy H(A|B). As one of the most elementary examples, we pick two maximal abelian *-subalgebras A, B of the n × n complex matrices Mn(C), and show relations between h(A|B) and the entropy for unistochastic matrices. Also we show related results in the case of a pair of subfactors of a type II1 factor. 2010 Mathematics Subject Classification: 46L55, 46L37, 46L40.
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ISSN:0126-6705
2180-4206