Continuous Family of Invariant Subspaces for R-diagonal Operators
Functional Analysis
2009-11-07 v2 Operator Algebras
Spectral Theory
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.
Cite
@article{arxiv.math/0103129,
title = {Continuous Family of Invariant Subspaces for R-diagonal Operators},
author = {Piotr Sniady and Roland Speicher},
journal= {arXiv preprint arXiv:math/0103129},
year = {2009}
}
Comments
35 pages