{
  "id": "1712.05920",
  "version": "v1",
  "published": "2017-12-16T08:42:35.000Z",
  "updated": "2017-12-16T08:42:35.000Z",
  "title": "On character space of the algebra of BSE-functions",
  "authors": [
    "Mohammad Fozouni"
  ],
  "comment": "8 pages, To appear in \"Sahand Communications in Mathematical Analysis\"",
  "categories": [
    "math.FA"
  ],
  "abstract": "Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{\\rm{BSE}}(\\Delta(A))$ consisting of all BSE-functions on $\\Delta(A)$ where $\\Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterization of $\\Delta(C_{\\rm{BSE}}(\\Delta(A)))$ and in the general case we give a partial answer. Also, using the Fourier algebra, we show that $C_{\\rm{BSE}}(\\Delta(A))$ is not a $C^*$-algebra in general. Finally for some subsets $E$ of $A^*$, we define the subspace of BSE-like functions on $\\Delta(A)\\cup E$ and give a nice application of this space related to Goldstine's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-16T08:42:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H05",
      "46J10"
    ],
    "keywords": [
      "character space",
      "bse-functions",
      "non-empty locally compact hausdroff space",
      "commutative banach algebra",
      "goldstines theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}