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, cilt.73, ss.533-546, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 73 Konu: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.7900/jot.2014mar12.2055
  • Dergi Adı: JOURNAL OF OPERATOR THEORY
  • Sayfa Sayıları: ss.533-546

Özet

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.