Canadian Mathematical Society
Canadian Mathematical Society
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$R$-Diagonal Elements and Freeness With Amalgamation

Open Access article
 Printed: Apr 2001
  • Alexandru Nica
  • Dimitri Shlyakhtenko
  • Roland Speicher
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The concept of $R$-diagonal element was introduced in \cite{NS2}, 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 \cite{Sh1}.
MSC Classifications: 46L54 show english descriptions Free probability and free operator algebras 46L54 - Free probability and free operator algebras

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