Journal of Operator Theory

Volume 59, Issue 2, Spring 2008 pp. 277-308.

Bounded Toeplitz products on weighted Bergman spaces

Authors: Karel Stroethoff (1) and Dechao Zheng (2)
Author institution: (1) Department of Mathematical Sciences, University of Montana, Missoula, Montana 59812, U.S.A.
(2) Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240, U.S.A.

Summary: We consider the question for which square integrable analytic functions $f$ and $g$ on the unit disk the densely defined products $T_{f}T_{\overline{g}}$ are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unweighted Bergman space. We will furthermore completely describe when the Toeplitz product $T_{f}T_{\overline{g}}$ is invertible or Fredholm and prove results generalizing those we obtained for the unweighted Bergman space.

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