| Full text | |
| Author(s): |
Doucha, Michal
;
Kaufmann, Pedro L.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES; v. 105, n. 3, p. 21-pg., 2022-03-02. |
| Abstract | |
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) | |
| FAPESP's process: | 16/25574-8 - Geometry of Banach Spaces |
| Grantee: | Valentin Raphael Henri Ferenczi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 17/18623-5 - Project on geometry of Lipschitz-free spaces and their approximation properties |
| Grantee: | Pedro Levit Kaufmann |
| Support Opportunities: | Regular Research Grants |