Operator theory on noncommutative varieties
| dc.creator | Popescu, Gelu | |
| dc.date | 2005-07-07 | |
| dc.date | 2007-03-21 | |
| dc.date.accessioned | 2026-07-07T07:52:49Z | |
| dc.date.available | 2026-07-07T07:52:49Z | |
| dc.description | We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function is associated with any (constrained) row contraction. For pure constrained row contraction, we show that the characteristic function is a complete unitary invariant and provide a model. We also show that the curvature invariant and Euler characteristic asssociated with a Hilbert module generated by an arbitrary (resp. commuting) row contraction can be expressed only in terms of the corresponding (resp. constrained) characteristic function. We provide a commutant lifting theorem for pure constrained row contractions and obtain a Nevanlinna-Pick interpolation result in this setting. Our theory includes, in particular, the commutative and q-commutative cases, while the standard noncommutative dilation theory for row contractions serves as a "universal model". | |
| dc.description | Comments | |
| dc.identifier | https://arxiv.org/abs/math/0507158 | |
| dc.identifier | http://arxiv.org/abs/math/0507158 | |
| dc.identifier | Indiana Univ. Math. J. 55 (2) (2006), 389--442 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126021 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 47A20, 47A56, 47A13, 47A63 | |
| dc.title | Operator theory on noncommutative varieties | |
| dc.type | text |