Brown measure and iterates of the Aluthge transform for some operators arising from measurable actions
| dc.creator | Dykema, Ken | |
| dc.creator | Schultz, Hanne | |
| dc.date | 2005-12-09 | |
| dc.date | 2008-02-05 | |
| dc.date.accessioned | 2026-07-07T09:18:39Z | |
| dc.date.available | 2026-07-07T09:18:39Z | |
| dc.description | We consider the Aluthge transform $|T|^{1/2}U|T|^{1/2}$ of a Hilbert space operator $T$, where $T=U|T|$ is the polar decomposition of $T$. We prove that the map that sends $T$ to its Aluthge transform is continuous with respect to the norm topology and with respect to the $*$--SOT topology on bounded sets. We consider the special case in a tracial von Neumann algebra when $U$ implements an automorphism of the von Neumann algebra generated by the positive part $|T|$ of $T$, and we prove that the iterated Aluthge transform converges to a normal operator whose Brown measure agrees with that of $T$ (and we compute this Brown measure). This proof relies on a theorem that is an analogue of von Neumann's mean ergodic theorem, but for sums weighted by binomial coefficients. | |
| dc.description | 11 pages. The revision (of Feb. 2008) involves a change of title and a change of emphasis | |
| dc.identifier | https://arxiv.org/abs/math/0512197 | |
| dc.identifier | http://arxiv.org/abs/math/0512197 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154103 | |
| dc.subject | Operator Algebras | |
| dc.subject | 47A05 | |
| dc.title | Brown measure and iterates of the Aluthge transform for some operators arising from measurable actions | |
| dc.type | text |