# On the isomorphism question for complete Pick multiplier algebras

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Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra $\mv = \{f\big| V : f \in \cM d\}$, where $d$ is some integer or $\infty$, $\cM d$ is the multiplier algebra of the Drury-Arveson space $H^2 d$, and $V$ is a subvariety of the unit ball. For finite $d$ 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.

Autor: Matt Kerr; John E. McCarthy; Orr Shalit

Fuente: https://archive.org/