" Toeplitz Operators on Arveson and Dirichlet Spaces"




H. Turgay Kaptanoglu

Bilkent University

Department of Mathematics




Abstract: We define Toeplitz operators on all Dirichlet spaces on the unit ball of CN and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms.
Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces.

(This is joint work with Daniel Alpay.)



Date:  Thursday, October 19, 2006

Time: 14.40

Place: Mathematics Seminar Room, SAZ-141