{
  "id": "1803.04672",
  "version": "v1",
  "published": "2018-03-13T08:05:47.000Z",
  "updated": "2018-03-13T08:05:47.000Z",
  "title": "On closed non-vanishing ideals in $C_B(X)$ II; compactness properties",
  "authors": [
    "A. Khademi",
    "M. R. Koushesh"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For a completely regular space $X$, let $C_B(X)$ be the normed algebra of all bounded continuous scalar-valued mappings on $X$ equipped with pointwise addition and multiplication and the supremum norm and let $C_0(X)$ be its subalgebra consisting of mappings vanishing at infinity. For a non-vanishing closed ideal $H$ of $C_B(X)$ we study properties of its spectrum $\\mathfrak{sp}(H)$ which may be characterized as the unique locally compact (Hausdorff) space $Y$ such that $H$ and $C_0(Y)$ are isometrically isomorphic. We concentrate on compactness properties of $\\mathfrak{sp}(H)$ and find necessary and sufficient (algebraic) conditions on $H$ such that the spectrum $\\mathfrak{sp}(H)$ satisfies (topological) properties such as the Lindel\\\"{o}f property, $\\sigma$-compactness, countable compactness, pseudocompactness and paracompactness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-13T08:05:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compactness properties",
      "closed non-vanishing ideals",
      "supremum norm",
      "regular space",
      "study properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}