Divisible operators in von Neumann algebras
| dc.creator | Sherman, David | |
| dc.date | 2006-11-13 | |
| dc.date | 2008-06-09 | |
| dc.date.accessioned | 2026-07-07T09:43:09Z | |
| dc.date.available | 2026-07-07T09:43:09Z | |
| dc.description | Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if (W*(x)' cap M) unitally contains a factor of type I_n. We decide the density of the n-divisible operators, for various n, M, and operator topologies. The most sensitive case is sigma-strong density in II_1 factors, which is closely related to the McDuff property. We make use of Voiculescu's noncommutative Weyl-von Neumann theorem to obtain several descriptions of the norm closure of the n-divisible operators in B(ell^2). Here are two consequences: (1) in contrast to the reducible operators, of which they form a subset, the divisible operators are nowhere dense; (2) if an operator is a norm limit of divisible operators, it is actually a norm limit of unitary conjugates of a single divisible operator. This is related to our ongoing work on unitary orbits by the following theorem, which is new even for B(ell^2): if an element of a von Neumann algebra belongs to the norm closure of the aleph_0-divisible operators, then the sigma-weak closure of its unitary orbit is convex. | |
| dc.description | 37 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611364 | |
| dc.identifier | http://arxiv.org/abs/math/0611364 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162448 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 47C15 (Primary); 47A65, 46L10 (Secondary) | |
| dc.title | Divisible operators in von Neumann algebras | |
| dc.type | text |