Continuous Family of Invariant Subspaces for R-diagonal Operators

Details Continuous Family of Invariant Subspaces for R-diagonal Operators Continuous Family of Invariant Subspaces for R-diagonal Operators

2001-03-21

arxiv.org/abs/math/0103129v2

Invent. Math. 146 (2001), no. 2, 329-363

Mathematics

Functional Analysis

35 pages

Scientific paper

10.1007/s002220100166

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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