Invariant Subspaces for Operators in a General II_1-factor
| dc.creator | Haagerup, Uffe | |
| dc.creator | Schultz, Hanne | |
| dc.date | 2006-11-09 | |
| dc.date.accessioned | 2026-07-07T07:32:41Z | |
| dc.date.available | 2026-07-07T07:32:41Z | |
| dc.description | It is shown that to every operator T in a general von Neumann factor M of type II_1 and to every Borel set B in the complex plane, one can associate a largest, closed, T-invariant subspace, K = K_T(B), affiliated with M, such that the Brown measure of T|_K is concentrated on B. Moreover, K is T-hyperinvariant, and the Brown measure of (1-P_K)T|_(1-P_K)(H) is concentrated on C\B. In particular, if T has a Brown measure which is not concentrated on a singleton, then there exists a non-trivial, closed, T-hyperinvariant subspace. Furthermore, it is shown that for every T in M, the limit A=\lim_{n\to\infty}[(T^n)* T^n]^{1/2n} exists in the strong operator topology and K_T(\bar{B(0,r)})=1_{[0,r]}(A), r>0. | |
| dc.description | 83 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611256 | |
| dc.identifier | http://arxiv.org/abs/math/0611256 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119198 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 47A15; 47C15; 46L54 | |
| dc.title | Invariant Subspaces for Operators in a General II_1-factor | |
| dc.type | text |