On continuous embeddings of quantum Sobolev spaces into Schatten classes $\mathfrak{H}_γ^{s,p}(G,H) \hookrightarrow S_p(H)$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914100376764416 |
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| author | Plakhotnikov, Alexander |
| author_facet | Plakhotnikov, Alexander |
| contents | This work investigates continuous embeddings for quantum Sobolev spaces $\mathfrak{H}_γ^{s,p}(G,H)$ into Schatten--von Neumann classes $S_r(H)$. We try to extend the results of Lakmon and Mensah to the case where the operators belong to Schatten classes $S_p(H)$ for $p \neq 2$. We establish that these quantum Sobolev spaces are Banach spaces and, by employing a duality argument, we define spaces for $p>2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On continuous embeddings of quantum Sobolev spaces into Schatten classes $\mathfrak{H}_γ^{s,p}(G,H) \hookrightarrow S_p(H)$ Plakhotnikov, Alexander Functional Analysis 47B90, 43A25, 47A62 This work investigates continuous embeddings for quantum Sobolev spaces $\mathfrak{H}_γ^{s,p}(G,H)$ into Schatten--von Neumann classes $S_r(H)$. We try to extend the results of Lakmon and Mensah to the case where the operators belong to Schatten classes $S_p(H)$ for $p \neq 2$. We establish that these quantum Sobolev spaces are Banach spaces and, by employing a duality argument, we define spaces for $p>2$. |
| title | On continuous embeddings of quantum Sobolev spaces into Schatten classes $\mathfrak{H}_γ^{s,p}(G,H) \hookrightarrow S_p(H)$ |
| topic | Functional Analysis 47B90, 43A25, 47A62 |
| url | https://arxiv.org/abs/2509.24135 |