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| मुख्य लेखकों: | , , , |
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| स्वरूप: | Preprint |
| प्रकाशित: |
2025
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| विषय: | |
| ऑनलाइन पहुंच: | https://arxiv.org/abs/2506.09786 |
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| _version_ | 1866912424956788736 |
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| author | Albiac, Fernando Ansorena, José L. Bíma, Jan Cúth, Marek |
| author_facet | Albiac, Fernando Ansorena, José L. Bíma, Jan Cúth, Marek |
| contents | The geometric analysis of non-locally convex quasi-Banach spaces presents rich and nuanced challenges. In this paper, we introduce the Schur $p$-property and the strong Schur $p$-property for $0 < p \leq 1$, providing new tools to deepen the understanding of these spaces, and the Lipschitz free $p$-spaces in particular. Moreover, by developing an adapted version of the compact reduction principle, we prove that Lipschitz free $p$-spaces over discrete metric spaces possess the approximation property, thereby answering positively a question raised by Albiac et al. in arXiv:2005.06555v2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz free $p$-spaces for $0<p<1$ in the light of the Schur $p$-property and the compact reduction Albiac, Fernando Ansorena, José L. Bíma, Jan Cúth, Marek Functional Analysis 46B03 (Primary), 46B07, 46B10, 46B15, 46B20, 46B25, 46B42, 46B08, 46E30, 46E40 (Secondary) The geometric analysis of non-locally convex quasi-Banach spaces presents rich and nuanced challenges. In this paper, we introduce the Schur $p$-property and the strong Schur $p$-property for $0 < p \leq 1$, providing new tools to deepen the understanding of these spaces, and the Lipschitz free $p$-spaces in particular. Moreover, by developing an adapted version of the compact reduction principle, we prove that Lipschitz free $p$-spaces over discrete metric spaces possess the approximation property, thereby answering positively a question raised by Albiac et al. in arXiv:2005.06555v2. |
| title | Lipschitz free $p$-spaces for $0<p<1$ in the light of the Schur $p$-property and the compact reduction |
| topic | Functional Analysis 46B03 (Primary), 46B07, 46B10, 46B15, 46B20, 46B25, 46B42, 46B08, 46E30, 46E40 (Secondary) |
| url | https://arxiv.org/abs/2506.09786 |