Local complementation in Banach spaces and its preservation under free constructions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929422915862528 |
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| author | Avilés, Antonio Martínez-Cervantes, Gonzalo Zoca, Abraham Rueda |
| author_facet | Avilés, Antonio Martínez-Cervantes, Gonzalo Zoca, Abraham Rueda |
| contents | In this work we consider natural generalizations of local complementation in Banach spaces, which include Lipschitz-local complementation. We show that all these notions are indeed equivalent to the classical notion of local complementation of Banach spaces. As an application, we show that local complementation is naturally preserved under certain free constructions in Functional Analysis, including Lipschitz-free spaces and free Banach lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_11339 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Local complementation in Banach spaces and its preservation under free constructions Avilés, Antonio Martínez-Cervantes, Gonzalo Zoca, Abraham Rueda Functional Analysis 46B07, 46B20, 46B40, 46B42 In this work we consider natural generalizations of local complementation in Banach spaces, which include Lipschitz-local complementation. We show that all these notions are indeed equivalent to the classical notion of local complementation of Banach spaces. As an application, we show that local complementation is naturally preserved under certain free constructions in Functional Analysis, including Lipschitz-free spaces and free Banach lattices. |
| title | Local complementation in Banach spaces and its preservation under free constructions |
| topic | Functional Analysis 46B07, 46B20, 46B40, 46B42 |
| url | https://arxiv.org/abs/2107.11339 |