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Autores principales: Ahmed, Hamidul, Das, B. Krishna, Sahu, Chaman Kumar
Formato: Preprint
Publicado: 2025
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Acceso en línea:https://arxiv.org/abs/2507.21537
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author Ahmed, Hamidul
Das, B. Krishna
Sahu, Chaman Kumar
author_facet Ahmed, Hamidul
Das, B. Krishna
Sahu, Chaman Kumar
contents We investigate isometric and algebraic isomorphism problems for multiplier algebras associated with Dirichlet series kernels that possess the complete Nevanlinna-Pick (CNP) property. A central aspect of our work is the explicit determination of the multiplier variety associated with each CNP Dirichlet series kernel, via polynomial equations derived from the arithmetic structure of the associated weight and frequency data. This description of multiplier varieties enables us to classify when the multiplier algebras of a signifincant class of CNP Dirichlet series kernels are isomorphic, or isometrically isomorphic. In this setting, a striking rigidity phenomenon emerges whereby the multiplier algebra determines the kernel up to natural equivalence. The results established for CNP Dirichlet series kernels also extend to classical CNP kernels, yielding new results for the associated multiplier algebras even in the classical setting. As an application, we resolve an open problem posed by McCarthy and Shalit ([19]).
format Preprint
id arxiv_https___arxiv_org_abs_2507_21537
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Multiplier varieties and multiplier algebras of CNP Dirichlet series kernels
Ahmed, Hamidul
Das, B. Krishna
Sahu, Chaman Kumar
Functional Analysis
Operator Algebras
14M10, 11M41, 47L15, 47A57, 46E22
We investigate isometric and algebraic isomorphism problems for multiplier algebras associated with Dirichlet series kernels that possess the complete Nevanlinna-Pick (CNP) property. A central aspect of our work is the explicit determination of the multiplier variety associated with each CNP Dirichlet series kernel, via polynomial equations derived from the arithmetic structure of the associated weight and frequency data. This description of multiplier varieties enables us to classify when the multiplier algebras of a signifincant class of CNP Dirichlet series kernels are isomorphic, or isometrically isomorphic. In this setting, a striking rigidity phenomenon emerges whereby the multiplier algebra determines the kernel up to natural equivalence. The results established for CNP Dirichlet series kernels also extend to classical CNP kernels, yielding new results for the associated multiplier algebras even in the classical setting. As an application, we resolve an open problem posed by McCarthy and Shalit ([19]).
title Multiplier varieties and multiplier algebras of CNP Dirichlet series kernels
topic Functional Analysis
Operator Algebras
14M10, 11M41, 47L15, 47A57, 46E22
url https://arxiv.org/abs/2507.21537