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Spectral constants for the quantum annulus
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Spectral constants for the quantum annulus

Sourav Pal, James E Pascoe and Nitin Tomar
ArXiv.org
24 Jan 2026
url
https://doi.org/10.48550/arxiv.2601.17560View
Preprint (Author's original)arXiv.org - Non-exclusive license to distribute Open

Abstract

Mathematics - Complex Variables Mathematics - Functional Analysis Mathematics - Operator Algebras
We find several new estimates for the spectral constants$K(\mathbb A_r)$for which a closed annulus$\overline{\mathbb A}_r$or closed polyannulus$\overline{\mathbb A}^n_r$is a$K$ -spectral set for operators in the quantum annulus$\mathbb Q \mathbb A_r$ . We give two alternative proofs to an existing estimate of spectral constant. The first proof capitalizes a dilation theorem due to McCullough and Pascoe, while the second proof involves a certain variety in the Euclidean biball. For commuting and doubly commuting operators in$\mathbb Q \mathbb A_r$ , we find upper and lower bounds for the smallest spectral constants.

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