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arXiv · 1505.05108

On the isomorphism problem for multiplier algebras of Nevanlinna-Pick spaces

Michael Hartz
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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 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 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.

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Michael Hartz. 2016-04-30. On the isomorphism problem for multiplier algebras of Nevanlinna-Pick spaces. https://doi.org/10.4153/cjm-2015-050-6

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