Schatten-von Neumann classes of tensors of invariant operators
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908457432514560 |
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| author | Delgado, Julio Posada, Liliana Ruzhansky, Michael |
| author_facet | Delgado, Julio Posada, Liliana Ruzhansky, Michael |
| contents | In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on corresponding Schatten-von Neumann properties. In the second part we specialised on tensors of invariant operators. In the special case where a suitable Fourier analysis associated to a fixed partition of a Hilbert space into finite dimensional subspaces is available we also give the corresponding formulae in terms of symbols. We also give a sufficient condition for Dixmier traceability for a class of finite tensors of pseudo-differential operators on the flat torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15055 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schatten-von Neumann classes of tensors of invariant operators Delgado, Julio Posada, Liliana Ruzhansky, Michael Functional Analysis 47B10, 47A80 In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on corresponding Schatten-von Neumann properties. In the second part we specialised on tensors of invariant operators. In the special case where a suitable Fourier analysis associated to a fixed partition of a Hilbert space into finite dimensional subspaces is available we also give the corresponding formulae in terms of symbols. We also give a sufficient condition for Dixmier traceability for a class of finite tensors of pseudo-differential operators on the flat torus. |
| title | Schatten-von Neumann classes of tensors of invariant operators |
| topic | Functional Analysis 47B10, 47A80 |
| url | https://arxiv.org/abs/2507.15055 |