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math.FA2025
Hadamard multipliers of the Agler class
Greg Knese
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 necessaril…
math.FA2025
The Schur-Agler class in infinitely many variables
Greg Knese
We define the Schur-Agler class in infinite variables to consist of functions whose restrictions to finite dimensional polydisks belong to the Schur-Agler class. We show that a nat…
math.FA2025
Testing von Neumann inequalities with nilpotent matrices
Greg Knese
We give an elementary proof of the folklore result that the Agler norm of a function is determined by its norm on commuting tuples of nilpotent matrices. The proof is variation on…