Finite Riesz products and Ornstein non-inequalities on quantum tori
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910157594689536 |
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| author | Tantalakis, Christos P. Wojciechowski, Michał |
| author_facet | Tantalakis, Christos P. Wojciechowski, Michał |
| contents | We demonstrate a construction of products on the quantum torus $\mathbb{T}_θ^2$ that generalises the usual construction of finite Riesz products on the commutative torus $\mathbb{T}^2$. We explain why the former constitutes a natural analogue of the latter in the non-commutative setting and, based on this construction, as well as on previous results by K. Kazaniecki and the second author, we prove a non-commutative version of an Ornstein non-inequality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20774 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite Riesz products and Ornstein non-inequalities on quantum tori Tantalakis, Christos P. Wojciechowski, Michał Operator Algebras Functional Analysis Primary 46L51, 46L52, Secondary: 42A55 We demonstrate a construction of products on the quantum torus $\mathbb{T}_θ^2$ that generalises the usual construction of finite Riesz products on the commutative torus $\mathbb{T}^2$. We explain why the former constitutes a natural analogue of the latter in the non-commutative setting and, based on this construction, as well as on previous results by K. Kazaniecki and the second author, we prove a non-commutative version of an Ornstein non-inequality. |
| title | Finite Riesz products and Ornstein non-inequalities on quantum tori |
| topic | Operator Algebras Functional Analysis Primary 46L51, 46L52, Secondary: 42A55 |
| url | https://arxiv.org/abs/2604.20774 |