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R-Diagonal Elements and Freeness With Amalgamation

Published online by Cambridge University Press:  20 November 2018

Alexandru Nica
Department of Pure Mathematics University of Waterloo Waterloo, Ontario N2L 3G1, e-mail:
Dimitri Shlyakhtenko
Department of Mathematics University of California at Los Angeles Los Angeles, California 90095-1555 U.S.A., e-mail:
Roland Speicher
Institut für Angewandte Mathematik Universität Heidelberg, Germany
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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].


Research Article
Copyright © Canadian Mathematical Society 2001


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