Colloquium

Compactness of Toeplitz operators on

pseudoconvex domains in Cn

Dr. Zeljko Cuckovic

University of Toledo

Abstract: The well-known AxlerZheng theorem characterizes compactness of finite sums of finite products of Toeplitz operators on the unit disk in terms of the Berezin transform of these operators. Subsequently this theorem was generalized to other domains, including the unit ball and polydisk in Cn.

In this work, we study the compactness of Toeplitz operators on weighted Bergman spaces on smooth bounded pseudoconvex domains.

 We prove a local version of the AxlerZheng theorem characterizing compactness of Toeplitz operators in the algebra generated by symbols continuous up to the boundary in terms of the behavior of the Berezin transform at strongly pseudoconvex points.

 This is a joint work with Sonmez Sahutoglu and Yunus Zeytuncu.