| Texto completo | |
| Autor(es): |
Doucha, Michal
;
Kaufmann, Pedro L.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES; v. 105, n. 3, p. 21-pg., 2022-03-02. |
| Resumo | |
We study Lipschitz-free spaces over compact and uniformly discrete metric spaces enjoying certain high regularity properties - having group structure with left-invariant metric. Using methods of harmonic analysis we show that, given a compact metrizable group G$G$ equipped with an arbitrary compatible left-invariant metric d$d$, the Lipschitz-free space over G$G$, F(G,d)$\mathcal {F}(G,d)$, satisfies the metric approximation property. We show also that, given a finitely generated group G$G$, with its word metric d$d$, from a class of groups admitting a certain special type of combing, which includes all hyperbolic groups and Artin groups of large type, F(G,d)$\mathcal {F}(G,d)$ has a Schauder basis. Examples and applications are discussed. In particular, for any net N$N$ in a real hyperbolic n$n$-space Hn$\mathbb {H}<^>n$, F(N)$\mathcal {F}(N)$ has a Schauder basis. (AU) | |
| Processo FAPESP: | 16/25574-8 - Geometria dos espaços de Banach |
| Beneficiário: | Valentin Raphael Henri Ferenczi |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 17/18623-5 - Projeto em geometria dos espaços Lipschitz-livres e suas propriedades de aproximação |
| Beneficiário: | Pedro Levit Kaufmann |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |