Spectral finiteness, quantum norm continuity and classical points
Functional Analysis
2026-03-23 v3 Operator Algebras
Quantum Algebra
Representation Theory
Abstract
We prove various notions of uniform continuity for compact-quantum-group representations on Hilbert or Banach spaces equivalent to having finite spectrum, i.e. finitely many isotypic components. This generalizes the classical analogue for compact-group representations on Banach spaces, and relies in part on Riemann-Lebesgue-type decay properties for Fourier coefficients of elements in minimal tensor products with compact-quantum-group function algebras.
Cite
@article{arxiv.2603.12090,
title = {Spectral finiteness, quantum norm continuity and classical points},
author = {Alexandru Chirvasitu},
journal= {arXiv preprint arXiv:2603.12090},
year = {2026}
}
Comments
v3 makes a number of technical alterations (statement and proof of Theorem 0.3, Lemma 1.8), minor changes and reference updates; 13 pages + references