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VON NEUMANN ENTROPY AND RELATIVE POSITION BETWEEN SUBALGEBRAS

MARIE CHODA

Osaka Kyoiku University, Asahigaoka, Kashiwara 582-8582, Japan

https://doi.org/10.1142/S0129167X13500663Cited by:1 (Source: Crossref)

Abstract

In order to give numerical characterizations of the notion of "mutual orthogonality", we introduce two kinds of family of positive definite matrices for a unitary u in a finite von Neumann algebra M. They are arising from u naturally depending on the decompositions of M. One corresponds to the tensor product decomposition and the other does to the crossed product decomposition. By using the von Neumann entropy for these positive definite matrices, we characterize the notion of mutual orthogonality between subalgebras.

Keywords:

AMSC: 46L55, 46L37, 46L40

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