On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces

By Michael Hartz. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2015

66 citations recorded by the source corpus.

Abstract We continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with the restrictions of a universal space, namely the Drury-Arveson space. Instead, we work directly with the Hilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic.This generalizes results of Davidson, Ramsey,Shalit, and the author.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d01b90000bb7680461c4aa0aca38fcb30111d078

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In Algebra and Number Theory

1. Raphael Clouatre
2. Michael Hartz

In Applied Mathematics

1. Raphael Clouatre
2. Michael Hartz

In Mathematical Physics

1. Raphael Clouatre
2. Michael Hartz

Citations in the corpus

• Multiplier algebras of complete Nevanlinna–Pick spaces: Dilations, boundary representations and hyperrigidity (2016, background): “Moreover, they fit in well with the recent interest in operator algebras associated to geometric varieties [23, 24, 35].”