{
  "id": "2005.08089",
  "version": "v1",
  "published": "2020-05-16T20:20:36.000Z",
  "updated": "2020-05-16T20:20:36.000Z",
  "title": "A Weak Form of Amenability of Topological Semigroups and its Applications in Ergodic and Fixed Point Theories",
  "authors": [
    "Ali Jabbari",
    "Ali Ebadian",
    "Madjid Eshaghi Gordji"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we introduce a weak form of amenability on topological semigroups that we call $\\varphi$-amenability, where $\\varphi$ is a character on a topological semigroup. Some basic properties of this new notion are obtained and by giving some examples, we show that this definition is weaker than the amenability of semigroups. As a noticeable result, for a topological semigroup $S$, it is shown that if $S$ is $\\varphi$-amenable, then $S$ is amenable. Moreover, $\\varphi$-ergodicity for a topological semigroup $S$ is introduced and it is proved that under some conditions on $S$ and a Banach space $X$, $\\varphi$-amenability and $\\varphi$-ergodicity of any antirepresntation defined by a right action $S$ on $X$, are equivalent. A relation between $\\varphi$-amenability of topological semigroups and existance of a common fixed point is investigated and by this relation, Hahn-Banach property of topological semigroups in the sense of $\\varphi$-amenability defined and studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-16T20:20:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A07",
      "22D15",
      "22A20"
    ],
    "keywords": [
      "topological semigroup",
      "fixed point theories",
      "amenability",
      "weak form",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}