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.
| Comments: | Communications on Pure and Applied Analysis, To appear |
| Subjects: | Functional Analysis (math.FA); Complex Variables (math.CV); Operator Algebras (math.OA) |
| Cite as: | arXiv:2601.17560 [math.FA] |
| (or arXiv:2601.17560v2 [math.FA] for this version) | |
| https://doi.org/10.48550/arXiv.2601.17560 arXiv-issued DOI via DataCite |
From: Sourav Pal [view email]
[v1]
Sat, 24 Jan 2026 19:10:47 UTC (20 KB)
[v2]
Fri, 22 May 2026 17:08:57 UTC (20 KB)
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