{
  "id": "2104.11519",
  "version": "v1",
  "published": "2021-04-23T10:07:48.000Z",
  "updated": "2021-04-23T10:07:48.000Z",
  "title": "Projections in Lipschitz-free spaces induced by group actions",
  "authors": [
    "Marek Cúth",
    "Michal Doucha"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that given a compact group $G$ acting continuously on a metric space $M$ by bi-Lipschitz bijections with uniformly bounded norms, the Lipschitz-free space over the space of orbits $M/G$ (endowed with Hausdorff distance) is complemented in the Lipschitz-free space over $M$. We also investigate the more general case when $G$ is amenable, locally compact or SIN and its action has bounded orbits. Then we get that the space of Lipschitz functions $Lip_0(M/G)$ is complemented in $Lip_0(M)$. Moreover, if the Lipschitz-free space over $M$, $F(M)$, is complemented in its bidual, several sufficient conditions on when $F(M/G)$ is complemented in $F(M)$ are given. Some applications are discussed. The paper contains preliminaries on projections induced by actions of amenable groups on general Banach spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-23T10:07:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lipschitz-free space",
      "group actions",
      "projections",
      "general banach spaces",
      "paper contains preliminaries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}