Complex symmetric Toeplitz operators on the weighted Bergman space

Abstract

In this paper, we give a characterization of a complex symmetric Toeplitz operator (Formula presented.) on the weighted Bergman space (Formula presented.). We first give properties of complex symmetric Toeplitz operators (Formula presented.) on (Formula presented.). Next, we prove that if (Formula presented.) is complex symmetric with finite symbol, then (Formula presented.) is hyponormal on (Formula presented.) if and only if it is hyponormal on the Hardy space (Formula presented.). Finally, we consider the complex symmetric Toeplitz operator (Formula presented.) on (Formula presented.) when the conjugation is a special case. © 2021 Informa UK Limited, trading as Taylor & Francis Group.