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arXiv · 2502.01999

Hadamard multipliers of the Agler class

Greg Knese
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Abstract

We prove several results about functions which preserve the Schur-Agler class under Hadamard or coefficient-wise product. First, functions which preserve the Schur class necessarily preserve the Schur-Agler class. Second, ``moments'' of certain commuting operator tuples form coefficients of Schur-Agler class preservers. Finally, any preserver of the full matrix Schur-Agler class must have coefficients given by moments of commuting operator tuples. We also point out that any counterexample to the multivariable von Neumann inequality can be used to derive a non-trivial Agler class preserver.

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Greg Knese. 2025-02-04. Hadamard multipliers of the Agler class. https://doi.org/10.1007/s00020-025-02799-6

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