On free resolutions in multivariable operator theory
| dc.creator | Greene, Devin C. V. | |
| dc.date | 2001-09-17 | |
| dc.date | 2001-09-18 | |
| dc.date.accessioned | 2026-07-07T04:43:24Z | |
| dc.date.available | 2026-07-07T04:43:24Z | |
| dc.description | We define the notion of a free resolution of a d-tuple $(T_1, T_2, . . . T_d)$ of mutually commuting operators acting on a Hilbert space H, and that this invariant gives rise to a class of vector space complexes parametrized by points in the unit ball $B_d = {z \in C^d: |z| <1}$. We show that for $λ\in B_d$ the homology of the corresponding complex is equivalent to the homology of the Koszul complex of a Mobius transform of $(T_1, T_2, . . . T_d)$. The notion of a Mobius transform in multivariable operator is defined, and some of its properties are investigated. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0109111 | |
| dc.identifier | http://arxiv.org/abs/math/0109111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62209 | |
| dc.subject | Functional Analysis | |
| dc.subject | Complex Variables | |
| dc.subject | Operator Algebras | |
| dc.subject | 47A13; 32A22; 18G10 | |
| dc.title | On free resolutions in multivariable operator theory | |
| dc.type | text |