The Free Cover of a Row Contraction
| dc.creator | Arveson, William | |
| dc.date | 2004-03-15 | |
| dc.date | 2004-04-15 | |
| dc.date.accessioned | 2026-07-07T05:06:24Z | |
| dc.date.available | 2026-07-07T05:06:24Z | |
| dc.description | We establish the existence and uniqueness of finite free resolutions - and their attendant Betti numbers - for graded commuting d-tuples of Hilbert space operators. Our approach is based on the notion of free cover of a (perhaps noncommutative) row contraction. Free covers provide a flexible replacement for minimal dilations that is better suited for higher-dimensional operator theory. For example, every graded d-contraction that is finitely multi-cyclic has a unique free cover of finite type - whose kernel is a Hilbert module inheriting the same properties. This contrasts sharply with what can be achieved by way of dilation theory (see Remark 2.4). | |
| dc.description | Added clarifying remarks, and examples of free resolutions. Aside from the examples, there is no substantial change in mathematical content | |
| dc.identifier | https://arxiv.org/abs/math/0403231 | |
| dc.identifier | http://arxiv.org/abs/math/0403231 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70454 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L07, 47A99 | |
| dc.title | The Free Cover of a Row Contraction | |
| dc.type | text |