Finite dimensional quotients of commutative operator algebras
| dc.creator | Meyer, Ralf | |
| dc.date | 1997-10-17 | |
| dc.date.accessioned | 2026-07-07T03:24:39Z | |
| dc.date.available | 2026-07-07T03:24:39Z | |
| dc.description | The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital operator algebras. This allows to define invariant distances on the spectrum of commutative operator algebras analogous to the Caratheodory distance for complex manifolds. Moreover, unitizations of two-dimensional operator algebras with zero multiplication provide a rich class of counterexamples. Especially, several badly behaved quotients of function algebras are exhibited. Recently, Arveson has developed a model theory for d-contractions. Quotients of the operator algebra of the d-shift are much more well-behaved than quotients of function algebras. Completely isometric representations of these quotients are obtained explicitly. This provides a generalization of Nevanlinna-Pick theory. An important property of quotients of the d-shift algebra is that their quotients of finite dimension r have completely isometric representations by rxr-matrices. Finally, the class of commutative operator algebras with this property is investigated. | |
| dc.description | 47 pages, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/funct-an/9710001 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9710001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33410 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | Finite dimensional quotients of commutative operator algebras | |
| dc.type | text |