ON THE C*-ALGEBRA GENERATED BY TOEPLITZ OPERATORS AND FOURIER MULTIPLIERS ON THE HARDY SPACE OF A LOCALLY COMPACT GROUP


Gul U.

JOURNAL OF OPERATOR THEORY, vol.73, no.2, pp.533-546, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.7900/jot.2014mar12.2055
  • Title of Journal : JOURNAL OF OPERATOR THEORY
  • Page Numbers: pp.533-546

Abstract

Let G be a locally compact abelian Hausdorff topological group which is non-compact and whose Pontryagin dual Gamma is partially ordered. Let Gamma(+) subset of Gamma be the semigroup of positive elements in Gamma. The Hardy space H-2(G) is the closed subspace of L-2 (G) consisting of functions whose Fourier transforms are supported on Gamma(+). In this paper we consider the C*-algebra C*(T(G) boolean OR F(C(Gamma(+)))) generated by Toeplitz operators with continuous symbols on G which vanish at infinity and Fourier multipliers with symbols which are continuous on one point compactification of Gamma(+) on the Hilbert-Hardy space H-2(G). We characterize the character space of this C*-algebra using a theorem of Power.