Remarks on free mutual information and orbital free entropy

Masaki Izumi, Yoshimichi Ueda

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)45-66
Number of pages22
JournalNagoya Mathematical Journal
Volume220
Issue number1
DOIs
Publication statusPublished - Jan 1 2015

Fingerprint

Free Entropy
Mutual Information
Subordination
Projection
Observation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Remarks on free mutual information and orbital free entropy. / Izumi, Masaki; Ueda, Yoshimichi.

In: Nagoya Mathematical Journal, Vol. 220, No. 1, 01.01.2015, p. 45-66.

Research output: Contribution to journalArticle

Izumi, Masaki ; Ueda, Yoshimichi. / Remarks on free mutual information and orbital free entropy. In: Nagoya Mathematical Journal. 2015 ; Vol. 220, No. 1. pp. 45-66.
@article{ee44ad454b98497cb09bb243ac449686,
title = "Remarks on free mutual information and orbital free entropy",
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.",
author = "Masaki Izumi and Yoshimichi Ueda",
year = "2015",
month = "1",
day = "1",
doi = "10.1215/00277630-3335530",
language = "English",
volume = "220",
pages = "45--66",
journal = "Nagoya Mathematical Journal",
issn = "0027-7630",
publisher = "Nagoya University",
number = "1",

}

TY - JOUR

T1 - Remarks on free mutual information and orbital free entropy

AU - Izumi, Masaki

AU - Ueda, Yoshimichi

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84952361304&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952361304&partnerID=8YFLogxK

U2 - 10.1215/00277630-3335530

DO - 10.1215/00277630-3335530

M3 - Article

VL - 220

SP - 45

EP - 66

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

IS - 1

ER -