Lack of isomorphic embeddings of $\ell_{p,q}$ into $L_{p,q}(\mathcal{M},τ)$ over a noncommutative probability space
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917636050255872 |
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| author | Huang, Jinghao Sadovskaya, Olga Sukochev, Fedor Zanin, Dmitriy |
| author_facet | Huang, Jinghao Sadovskaya, Olga Sukochev, Fedor Zanin, Dmitriy |
| contents | We prove that the sequence space $\ell_{p,q}$ does not embed into $L_{p,q}(\mathcal{M},τ)$ for any noncommutative probability space $(\mathcal{M},τ)$, $1< p<\infty $, $1\le q<\infty$, $p\ne q$. Several applications to the isomorphic classification of noncommutative $L_{p,q}$-spaces are given, which extend and complement several earlier results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06761 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lack of isomorphic embeddings of $\ell_{p,q}$ into $L_{p,q}(\mathcal{M},τ)$ over a noncommutative probability space Huang, Jinghao Sadovskaya, Olga Sukochev, Fedor Zanin, Dmitriy Operator Algebras Functional Analysis We prove that the sequence space $\ell_{p,q}$ does not embed into $L_{p,q}(\mathcal{M},τ)$ for any noncommutative probability space $(\mathcal{M},τ)$, $1< p<\infty $, $1\le q<\infty$, $p\ne q$. Several applications to the isomorphic classification of noncommutative $L_{p,q}$-spaces are given, which extend and complement several earlier results. |
| title | Lack of isomorphic embeddings of $\ell_{p,q}$ into $L_{p,q}(\mathcal{M},τ)$ over a noncommutative probability space |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2404.06761 |