TY - JOUR

T1 - On the Isomorphism Question for Complete Pick Multiplier Algebras

AU - Kerr, Matt

AU - McCarthy, John E.

AU - Shalit, Orr Moshe

N1 - Funding Information:
The first author was partially supported by National Science Foundation Grant DMS 1068974. The second author was partially supported by National Science Foundation Grant DMS 0966845. The third author was partially supported by Israel Science Foundation Grant no. 474/12 and by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 321749.

PY - 2013/5/1

Y1 - 2013/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84876096266&partnerID=8YFLogxK

U2 - 10.1007/s00020-013-2048-2

DO - 10.1007/s00020-013-2048-2

M3 - Article

AN - SCOPUS:84876096266

VL - 76

SP - 39

EP - 53

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -