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).
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Louhichi, I., Strouse, E. & Zakariasy, L. Products of Toeplitz Operators on the Bergman Space. Integr. equ. oper. theory 54, 525–539 (2006). https://doi.org/10.1007/s00020-005-1369-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00020-005-1369-1