Continuous family of invariant subspaces for R–diagonal operators
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- Śniady, P. & Speicher, R. Invent. math. (2001) 146: 329. doi:10.1007/s002220100166
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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.