Abstract:
We study by the function theory on Cartan domains, the Berezin-Toeplitz symbol
calculus, the essential commutant of analytic Toeplitz operators and algebras associated
with spherical isometries and on the Bergman space. The classification of reducing
subspaces of a class of multiplication operators on the Bergman space, the Hardy space
of the bidisk with the Totally Abelian Toeplitz operators and geometric invariants
associated with their symbol curves are considered. The Hankel operators on Fock spaces
and related Bergman kernel estimates and asymptotics for generalized Fock spaces are
introduced . We obtain the localization, compactness and Sarason’s Toeplitz product
problem in Bergman and Fock spaces .
