Set theory and cyclic vectors
| dc.creator | Weaver, Nik | |
| dc.date | 2002-02-25 | |
| dc.date.accessioned | 2026-07-07T04:46:41Z | |
| dc.date.available | 2026-07-07T04:46:41Z | |
| dc.description | Let H be a separable, infinite dimensional Hilbert space and let S be a countable subset of H. Then most positive operators on H have the property that every nonzero vector in the span of S is cyclic, in the sense that the set of operators in the positive part of the unit ball of B(H) with this property is comeager for the strong operator topology. Suppose κis a regular cardinal such that κ\geq ω_1 and 2^{<κ} = κ. Then it is relatively consistent with ZFC that 2^ω= κand for any subset S \subset H of cardinality less than κthe set of positive operators in the unit ball of B(H) for which every nonzero vector in the span of S is cyclic is comeager for the strong operator topology. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0202265 | |
| dc.identifier | http://arxiv.org/abs/math/0202265 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63431 | |
| dc.subject | Functional Analysis | |
| dc.subject | Logic | |
| dc.subject | 03E35, 03E50, 47A15, 47A16 | |
| dc.title | Set theory and cyclic vectors | |
| dc.type | text |