Document Type
Article
Publication Date
5-1-2013
Abstract
Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra MV={f∣∣V:f∈Md}, where d is some integer or ∞,Md is the multiplier algebra of the Drury-Arveson space H2d , 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
Recommended Citation
Kerr, Matt; McCarthy, John E.; and Shalit, Orr Moshe, "On the Isomorphism Question for Complete Pick Multiplier Algebras" (2013). Mathematics Faculty Publications. 13.
https://openscholarship.wustl.edu/math_facpubs/13
Embargo Period
5-24-2014
Comments
This is a post-review author version. The final publication is available in Integral Equations and Operator Theory at link.springer.com. © Copyright 2013 Springer Basel. DOI: http://dx.doi.org/10.1007/s00020-013-2048-2