Compact reduction in Lipschitz-free spaces
[EN] We prove a general principle satisfied by weakly precompact sets of Lip-schitz-free spaces. By this principle, certain infinite-dimensional phenomena in Lipschitzfree spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy conseq...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/184747 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/184747 |
| Access Level: | acceso abierto |
| Palavra-chave: | Lipschitz-free space Lipschitz function Lipschitz lifting property Schur property Approximation property Weak sequential ompleteness Dunford-Pettis property TECNOLOGIA ELECTRONICA |
| Resumo: | [EN] We prove a general principle satisfied by weakly precompact sets of Lip-schitz-free spaces. By this principle, certain infinite-dimensional phenomena in Lipschitzfree spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. The main new results are: F(X) is weakly sequentially complete for every superreflexive Banach space X, and F(M) has the Schur property and the approximation property for every scattered complete metric space M. |
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