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R-Diagonal Elements and Freeness With Amalgamation

Published online by Cambridge University Press:  20 November 2018

Alexandru Nica ,
Dimitri Shlyakhtenko  and
Roland Speicher
Alexandru Nica
Affiliation:
Department of Pure Mathematics University of Waterloo Waterloo, Ontario N2L 3G1, e-mail: anica@math.uwaterloo.ca
Dimitri Shlyakhtenko
Affiliation:
Department of Mathematics University of California at Los Angeles Los Angeles, California 90095-1555 U.S.A., e-mail: shlyakht@math.ucla.edu
Roland Speicher
Affiliation:
Institut für Angewandte Mathematik Universität Heidelberg, Germany
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Abstract

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The concept of $R$-diagonal element was introduced in [5], and was subsequently found to have applications to several problems in free probability. In this paper we describe a new approach to $R$-diagonality, which relies on freeness with amalgamation. The class of $R$-diagonal elements is enlarged to contain examples living in non-tracial $*$-probability spaces, such as the generalized circular elements of [7].

Keywords

46L54
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 2 , 01 April 2001 , pp. 355 - 381
Copyright
Copyright © Canadian Mathematical Society 2001

References

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