Substochastic operators in symmetric spaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929383053197312 |
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| author | Ciesielski, Maciej Lewicki, Grzegorz |
| author_facet | Ciesielski, Maciej Lewicki, Grzegorz |
| contents | First, we solve a crucial problem under which conditions increasing uniform K-monotonicity is equivalent to lower locally uniform K-monotonicity. Next, we investigate properties of substochastic operators on $L^1+L^\infty$ with applications. Namely, we show that a countable infinite combination of substochastic operators is also substochastic. Using K-monotonicity properties, we prove several theorems devoted to the convergence of the sequence of substochastic operators in the norm of a symmetric space E under addition assumption on E. In our final discussion we focus on compactness of admissible operators for arbitrary Banach couples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Substochastic operators in symmetric spaces Ciesielski, Maciej Lewicki, Grzegorz Functional Analysis First, we solve a crucial problem under which conditions increasing uniform K-monotonicity is equivalent to lower locally uniform K-monotonicity. Next, we investigate properties of substochastic operators on $L^1+L^\infty$ with applications. Namely, we show that a countable infinite combination of substochastic operators is also substochastic. Using K-monotonicity properties, we prove several theorems devoted to the convergence of the sequence of substochastic operators in the norm of a symmetric space E under addition assumption on E. In our final discussion we focus on compactness of admissible operators for arbitrary Banach couples. |
| title | Substochastic operators in symmetric spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2406.08095 |