Autor(es)

Doucha, Michal ; Kaufmann, Pedro L.

• 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