Complex symmetric Toeplitz operators on the weighted Bergman space.

In this paper, we give a characterization of a complex symmetric Toeplitz operator T φ on the weighted Bergman space A α 2 (D). We first give properties of complex symmetric Toeplitz operators T φ on A α 2 (D). Next, we prove that if T φ is complex symmetric with finite symbol, then T φ is hyponormal on A α 2 (D) if and only if it is hyponormal on the Hardy space H 2 (T). Finally, we consider the complex symmetric Toeplitz operator T φ on A α 2 (D) when the conjugation is a special case. [ABSTRACT FROM AUTHOR]