On the Isomorphism Question for Complete Pick Multiplier Algebras

Matt Kerr, John E. McCarthy, Orr Moshe Shalit

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra MV = {f{pipe}V: f ∈ Md}, where d is some integer or ∞, Md is the multiplier algebra of the Drury-Arveson space Hd2, and V is a subvariety of the unit ball. For finite dimensional d it is known that, under mild assumptions, every isomorphism between two such algebras MV and MW is induced by a biholomorphism between W and V. In this paper we consider the converse, and obtain positive results in two directions. The first deals with the case where V is the proper image of a finite Riemann surface. The second deals with the case where V is a disjoint union of varieties.

Original languageEnglish
Pages (from-to)39-53
Number of pages15
JournalIntegral Equations and Operator Theory
Volume76
Issue number1
DOIs
StatePublished - 1 May 2013

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