Continuous family of invariant subspaces for R-diagonal operators

Authors
Sniady, P Speicher, R
Citation
P. Sniady et R. Speicher, Continuous family of invariant subspaces for R-diagonal operators, INVENT MATH, 146(2), 2001, pp. 329-363
Citations number
33
Categorie Soggetti
Mathematics
Journal title
INVENTIONES MATHEMATICAE
ISSN journal
00209910 → ACNP
Volume
146
Issue
2
Year of publication
2001
Pages
329 - 363
Database
ISI
SICI code
0020-9910(200111)146:2<329:CFOISF>2.0.ZU;2-P
Abstract
We show that every R-diagonal operator x has a continuous family of invaria nt subspaces relative to the von Neumann algebra generated by x. This allow s 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 n ew concept of R-diagonality with amalgamation, for which we give several eq uivalent characterizations.