Commuting squares and relative entropy for two subfactors

Yasuo Watatani; Jerzy Wierzbicki

doi:10.1006/jfan.1995.1128

Commuting squares and relative entropy for two subfactors

Yasuo Watatani, Jerzy Wierzbicki

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We compute Connes-Störmer relative entropy H(M/N) for two subfactors M and N of a type II₁ factor without assuming N ⊂ M. If they form a commuting square, then we have H(M/N) = H(M/M ∩ N). If their commutants form a commuting square, then we have H(M/N) = H(M ∨ N/N).

Original language	English
Pages (from-to)	329-341
Number of pages	13
Journal	Journal of Functional Analysis
Volume	133
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1995.1128
Publication status	Published - Nov 1 1995

All Science Journal Classification (ASJC) codes

Analysis

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10.1006/jfan.1995.1128

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title = "Commuting squares and relative entropy for two subfactors",

abstract = "We compute Connes-St{\"o}rmer relative entropy H(M/N) for two subfactors M and N of a type II1 factor without assuming N ⊂ M. If they form a commuting square, then we have H(M/N) = H(M/M ∩ N). If their commutants form a commuting square, then we have H(M/N) = H(M ∨ N/N).",

author = "Yasuo Watatani and Jerzy Wierzbicki",

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N2 - We compute Connes-Störmer relative entropy H(M/N) for two subfactors M and N of a type II1 factor without assuming N ⊂ M. If they form a commuting square, then we have H(M/N) = H(M/M ∩ N). If their commutants form a commuting square, then we have H(M/N) = H(M ∨ N/N).

AB - We compute Connes-Störmer relative entropy H(M/N) for two subfactors M and N of a type II1 factor without assuming N ⊂ M. If they form a commuting square, then we have H(M/N) = H(M/M ∩ N). If their commutants form a commuting square, then we have H(M/N) = H(M ∨ N/N).

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DO - 10.1006/jfan.1995.1128

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IS - 2

ER -

Commuting squares and relative entropy for two subfactors

Abstract

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