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Continuous Family of Invariant Subspaces for R-diagonal Operators

Piotr Sniady·Roland Speicher
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Abstract

We show that every R-diagonal operator x has a continuous family of invariant subspaces relative to the von Neumann algebra generated by x. This allows us to find the Brown measure of x and to find a new conceptual proof that Voiculescu's S-transform is multiplicative. Our considerations base on a new concept of R-diagonality with amalgamation, for which we give several equivalent characterizations.

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BibTeXRIS

Piotr Sniady, Roland Speicher. 2001-04-13. Continuous Family of Invariant Subspaces for R-diagonal Operators. https://doi.org/10.1007/s002220100166

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