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Remarks on free mutual information and orbital free entropy

Published online by Cambridge University Press:  11 January 2016

Masaki Izumi  and
Yoshimichi Ueda
Masaki Izumi
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, [email protected]
Yoshimichi Ueda
Affiliation:
Graduate School of Mathematics, Kyushu University, Fukuoka, 819-0395, [email protected]
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Abstract

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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.

Keywords

Primary 46L54Secondary 94A17
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 220 , December 2015 , pp. 45 - 66
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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