Remarks on free mutual information and orbital free entropy

Remarks on free mutual information and orbital free entropy

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....

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Veröffentlicht in:Nagoya mathematical journal 2015-12, Vol.220, p.45-66
Hauptverfasser: Izumi, Masaki, Ueda, Yoshimichi
Format: Artikel
Sprache:eng
Schlagworte:
46L54
94A17
Free mutual information
free SDE
liberation process
Loewner equation
orbital free entropy
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Zusammenfassung: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.
ISSN:0027-7630
2152-6842
DOI:10.1215/00277630-3335530