" Toeplitz Operators on Arveson and Dirichlet Spaces"
H. Turgay Kaptanoglu
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.).
Place: Mathematics Seminar Room, SAZ-141