Embeddability of ℓp and bases in Lipschitz free p-spaces for 0 < p ≤ 1
Our goal in this paper is to continue the study initiated by the authors in of the geometry of the Lipschitz free p-spaces over quasimetric spaces for 0 < p ≤ 1, denoted Fp(M). Here we develop new techniques to show that, by analogy with the case p = 1, the space p embeds isomorphically in Fp...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universidad Pública de Navarra |
| Repositorio: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/36849 |
| Acesso em linha: | https://hdl.handle.net/2454/36849 |
| Access Level: | acceso abierto |
| Palavra-chave: | Quasimetric space Quasi-Banach space Lipschitz free p-space Embedding of ℓp |
| Resumo: | Our goal in this paper is to continue the study initiated by the authors in of the geometry of the Lipschitz free p-spaces over quasimetric spaces for 0 < p ≤ 1, denoted Fp(M). Here we develop new techniques to show that, by analogy with the case p = 1, the space p embeds isomorphically in Fp(M) for 0 < p < 1. Going further we see that despite the fact that, unlike the case p = 1, this embedding need not be complemented in general, complementability of p in a Lipschitz free p-space can still be attained by imposing certain natural restrictions to M. As a by-product of our discussion on bases in Fp([0, 1]), we obtain examples of p-Banach spaces for p < 1 that are not based on a trivial modification of Banach spaces, which possess a basis but fail to have an unconditional basis. |
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