Some results for Toeplitz operators on the Bergman space

GÜRDAL M., SOHRET F.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.3, pp.789-793, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 218 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.1016/j.amc.2011.01.069
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.789-793
  • Keywords: Bergman space, Toeplitz operator, Berezin symbol, Hankel operator, Harmonic function, Reproducing kernel
  • Süleyman Demirel University Affiliated: Yes

Abstract

We consider the Toeplitz operators on the Bergman space L(a)(2)(D) on the unit disc D. In terms of reproducing kernels the invariant subspaces of Bergman space Toeplitz operator is studied. We also investigate invertibility of Toeplitz operators in terms of Berezin symbols. Moreover, the Hankel operators and Berezin symbols are used to characterize compactness of operators 2T(phi psi) - T(phi)T(psi) - T(psi)T(phi) for bounded harmonic functions phi and psi. (C) 2011 Elsevier Inc. All rights reserved.