Some H-Toeplitz operators on the Bergman space

Professor George Exner; Department of Mathematics, Bucknell University

The H-Toeplitz operators on the Bergman space (of complex-valued functions holomorphic and square integrable with respect to area measure on the unit disk in the complex plane) are defined with the aid of the subspace of harmonic functions. They have been studied, for certain symbols, for hyponormality or contractivity or their lacks. We provide structure theorems for some such H-Toeplitz operators which allow either improvement from hyponormality to subnormality or the even stronger property of being moment infinitely divisible, or render more transparent hyponormality and contractivity or their failures.  Essential to the study are the geometrically regular weighted shifts (GRWS) on Hilbert space and their representatives in classes of interest related to subnormality.

To participate in the seminar remotely via Zoom, go to https://uiowa.zoom.us/j/95316149275