Orlicz-Schatten Factorizations for Non-Commutative Sobolev Embeddings
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915295741870080 |
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| author | Sulaver, Emma |
| author_facet | Sulaver, Emma |
| contents | We develop a framework for factorizing embeddings of non-commutative Sobolev spaces on quantum tori through newly defined Orlicz-Schatten sequence ideals. After introducing appropriate non-commutative Sobolev norms and Orlicz spectral conditions, we establish a summing operator characterization of the quantum Laplacian embedding. Our main results provide both existence and optimality of such factorization theorems, and highlight connections to operator ideal theory. Applications to regularity of non-commutative PDEs and quantum information metrics are discussed, demonstrating the broad impact of these structures in functional analysis and mathematical physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_15085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orlicz-Schatten Factorizations for Non-Commutative Sobolev Embeddings Sulaver, Emma Functional Analysis Operator Algebras Spectral Theory 46L87, 46E35, 47B10 We develop a framework for factorizing embeddings of non-commutative Sobolev spaces on quantum tori through newly defined Orlicz-Schatten sequence ideals. After introducing appropriate non-commutative Sobolev norms and Orlicz spectral conditions, we establish a summing operator characterization of the quantum Laplacian embedding. Our main results provide both existence and optimality of such factorization theorems, and highlight connections to operator ideal theory. Applications to regularity of non-commutative PDEs and quantum information metrics are discussed, demonstrating the broad impact of these structures in functional analysis and mathematical physics. |
| title | Orlicz-Schatten Factorizations for Non-Commutative Sobolev Embeddings |
| topic | Functional Analysis Operator Algebras Spectral Theory 46L87, 46E35, 47B10 |
| url | https://arxiv.org/abs/2505.15085 |