Integral Equations and Operator Theory

, Volume 54, Issue 4, pp 525–539

Products of Toeplitz Operators on the Bergman Space

  • Issam Louhichi
  • Elizabeth Strouse
  • Lova Zakariasy
Original Paper

DOI: 10.1007/s00020-005-1369-1

Cite this article as:
Louhichi, I., Strouse, E. & Zakariasy, L. Integr. equ. oper. theory (2006) 54: 525. doi:10.1007/s00020-005-1369-1

Abstract.

In 1962 Brown and Halmos gave simple conditions for the product of two Toeplitz operators on Hardy space to be equal to a Toeplitz operator. Recently, Ahern and Cucković showed that a similar result holds for Toeplitz operators with bounded harmonic symbols on Bergman space. For general symbols, the situation is much more complicated. We give necessary and sufficient conditions for the product to be a Toeplitz operator (Theorem 6.1), an explicit formula for the symbol of the product in certain cases (Theorem 6.4), and then show that almost anything can happen (Theorem 6.7).

Mathematics Subject Classification (2000).

Primary 47B35Secondary 47L80

Keywords.

Toeplitz operatorsBergman spaceMellin transform

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Issam Louhichi
    • 1
  • Elizabeth Strouse
    • 1
  • Lova Zakariasy
    • 1
  1. 1.UFR de Mathématiques InformatiquesUniversité Bordeaux ITalenceFrance