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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2408.15208 |
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| _version_ | 1866911182872379392 |
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| author | Megrelishvili, Michael |
| author_facet | Megrelishvili, Michael |
| contents | We introduce a topometric version of Lipschitz-free spaces and study its universal property. Another aim of this paper is to investigate actions of topological groups $G$ on Lipschitz-free spaces $\mathcal{F}(M)$, induced by isometric actions on pointed metric spaces $M$. In particular, we study the associated dynamical $G$-systems under the weak-star topology, focusing on the dual action on $\mathrm{Lip}_0(M) = \mathcal{F}(M)^*$ and the bidual $\mathcal{F}(M)^{**}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lipschitz-Free Spaces: A Topometric Approach and Group Actions Megrelishvili, Michael Functional Analysis Dynamical Systems General Topology 46B04, 46B20, 43A65, 51F30, 53C23, 54H15 We introduce a topometric version of Lipschitz-free spaces and study its universal property. Another aim of this paper is to investigate actions of topological groups $G$ on Lipschitz-free spaces $\mathcal{F}(M)$, induced by isometric actions on pointed metric spaces $M$. In particular, we study the associated dynamical $G$-systems under the weak-star topology, focusing on the dual action on $\mathrm{Lip}_0(M) = \mathcal{F}(M)^*$ and the bidual $\mathcal{F}(M)^{**}$. |
| title | Lipschitz-Free Spaces: A Topometric Approach and Group Actions |
| topic | Functional Analysis Dynamical Systems General Topology 46B04, 46B20, 43A65, 51F30, 53C23, 54H15 |
| url | https://arxiv.org/abs/2408.15208 |