 |
|
$R$-Diagonal Elements and Freeness With Amalgamation |
Canad. J. Math. 53(2001), 355-381
Published:2001-04-01
Printed: Apr 2001
Printed: Apr 2001
- Alexandru Nica
- Dimitri Shlyakhtenko
- Roland Speicher
Abstract
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 - Free probability and free operator algebras |