Unitary perturbations of masas in type $II_1$ factors
| dc.creator | Sinclair, Allan M. | |
| dc.creator | Smith, Roger R. | |
| dc.date | 2001-11-30 | |
| dc.date.accessioned | 2026-07-07T04:44:54Z | |
| dc.date.available | 2026-07-07T04:44:54Z | |
| dc.description | We investigate maximal abelian subalgebras (masas) in separably acting type $II_1$ factors. We use the notion of distance between masas which we introduced in an earlier paper in this archive, OA/0107075. The main result of the paper is to show that for any unitary u and a masa A, the distance between A and uAu* is comparable to the distance in 2-norm from u to the unitary normalizer N(A) of A. In qualitative terms, this says that a unitary almost normalizes A if and only if it is close to a normalizing unitary. Inequalities in the paper make this statement quantitatively precise. As a consequence, all singular masas in separably acting type $II_1$ factors are $α$-strongly singular, as defined in the above referenced paper, for a universal value of $α$. | |
| dc.description | latex file, 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0111330 | |
| dc.identifier | http://arxiv.org/abs/math/0111330 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62782 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L10; 46L35 | |
| dc.title | Unitary perturbations of masas in type $II_1$ factors | |
| dc.type | text |