Spectral finiteness, quantum norm continuity and classical points
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915877367054336 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12090 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral finiteness, quantum norm continuity and classical points Chirvasitu, Alexandru Functional Analysis Operator Algebras Quantum Algebra Representation Theory 46L67, 22D10, 16T05, 16T15, 47B01, 43A32, 46L85, 47L65 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. |
| title | Spectral finiteness, quantum norm continuity and classical points |
| topic | Functional Analysis Operator Algebras Quantum Algebra Representation Theory 46L67, 22D10, 16T05, 16T15, 47B01, 43A32, 46L85, 47L65 |
| url | https://arxiv.org/abs/2603.12090 |