Operator algebras for analytic varieties
| dc.contributor.author | Davidson, Kenneth R. | |
| dc.contributor.author | Ramsey, Christopher | |
| dc.contributor.author | Shalit, Orr Moshe | |
| dc.date.accessioned | 2020-12-16 | |
| dc.date.accessioned | 2022-05-31T01:43:00Z | |
| dc.date.available | 2022-05-31T01:43:00Z | |
| dc.date.issued | 2015 | |
| dc.description.abstract | We study the isomorphism problem for the multiplier algebras of irreducible complete Pick kernels. These are precisely the restrictions MV of the multiplier algebra M of Drury-Arveson space to a holomorphic subvariety V of the unit ball Bd. We find that MV is completely isometrically isomorphic to MW if and only if W is the image of V under a biholomorphic automorphism of the ball. In this case, the isomorphism is unitarily implemented. This is then strengthened to show that, when d<∞, every isometric isomorphism is completely isometric. The problem of characterizing when two such algebras are (algebraically) isomorphic is also studied. When V and W are each a finite union of irreducible varieties and a discrete variety in Bd with d<∞, then an isomorphism between MV and MW determines a biholomorphism (with multiplier coordinates) between the varieties; and the isomorphism is composition with this function. These maps are automatically weak-∗ continuous. We present a number of examples showing that the converse fails in several ways. We discuss several special cases in which the converse does hold---particularly, smooth curves and Blaschke sequences. We also discuss the norm closed algebras associated to a variety, and point out some of the differences. | |
| dc.format.extent | 471.06KB | |
| dc.format.mimetype | ||
| dc.identifier.citation | Davidson, K., Ramsey, C. & Shalit, O. (2015). Operator algebras for analytic varieties. Transactions of the American Mathematical Society 367(2), 1121-1150. https://doi.org/10.1090/S0002-9947-2014-05888-1 | |
| dc.identifier.doi | https://doi.org/10.1090/S0002-9947-2014-05888-1 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14078/2098 | |
| dc.language | English | |
| dc.language.iso | en | |
| dc.rights | All Rights Reserved | |
| dc.subject | non-selfadjoint operator algebras | |
| dc.subject | reproducing kernel Hilbert spaces | |
| dc.title | Operator algebras for analytic varieties | en |
| dc.type | Article Post-Print | |
| dspace.entity.type |
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