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arXiv · 2505.08476

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

Sourav Pal·Nitin Tomar
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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 $\mathbb C^2$ 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.

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Sourav Pal, Nitin Tomar. 2025-05-13. Dilation on an annulus and von Neumann's inequality on certain varieties in the biball. https://arxiv.org/abs/2505.08476

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