Dilation on an annulus and von Neumann's inequality on certain varieties in the biball

2025/05/13 by Pal, Sourav, Tomar, Nitin
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2505.08476

Abstract

We give an alternative proof to Agler's famous result on success of rational dilation on an annulus by an application of a result due to Dritschel and McCullough. We show interplay between operators associated with an annulus, C_1,r or quantum annulus and operator pairs living on a certain variety in \mathbb C² and its intersection with the biball. It is shown that the minimal spectral sets and von Neumann's inequality for these classes C_1,r, quantum annulus can also be studied via appropriate operator pairs associated with the biball.

Citations

• Subinner-free outer factorizations on an annulus
• Geometric Dilations and Operator Annuli
• A von Neumann type inequality for an annulus
• Spectral Sets: Numerical Range and Beyond
• Dilations and constrained algebras
• Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on Complex Balls
• Bounded Point Evaluations and Local Spectral Theory

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