Commuting Squares and Relative Entropy for Two Subfactors

We compute Connes-Störmer relative entropy H( M/ N) for two subfactors M and N of a type II 1 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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Bibliographic Details
Published in:Journal of functional analysis 1995, Vol.133 (2), p.329-341
Main Authors: Watatani, Y., Wierzbicki, J.
Format: Article
Language:English
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Summary:We compute Connes-Störmer relative entropy H( M/ N) for two subfactors M and N of a type II 1 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).
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.1995.1128