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Remarks on free mutual information and orbital free entropy

Published online by Cambridge University Press:  11 January 2016

Masaki Izumi
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan izumi@math.kyoto-u.ac.jp
Yoshimichi Ueda
Affiliation:
Graduate School of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan ueda@math.kyushu-u.ac.jp
Corresponding
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Abstract

The present notes provide a proof of i* (ℂP + ℂ(I - P); ℂQ + ℂ(I - Q)) = – χorb(P,Q) for any pair of projections P,Q with τ(P) = τ(Q) = 1/2. The proof includes new extra observations, such as a subordination result in terms of Loewner equations. A study of the general case is also given.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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