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Preprint
Spectral constants for the quantum annulus
ArXiv.org
24 Jan 2026
Abstract
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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Details
- Title
- Spectral constants for the quantum annulus
- Creators
- Sourav Pal - Indian Institute of Technology BombayJames E Pascoe - Drexel University, MathematicsNitin Tomar - Indian Institute of Technology Bombay
- Publication Details
- ArXiv.org
- Number of pages
- 25
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022157470004721