On the isomorphism question for complete Pick multiplier algebras [article]

Matt Kerr, John E. McCarthy, Orr Shalit
2013 arXiv   pre-print
Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra = {f|_V : f ∈_d}, where d is some integer or ∞, _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 and 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
more » ... ls 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.
arXiv:1211.1116v2 fatcat:phcskb63ebchfmtguaqjlats3a