ANALYSIS
SEMINAR

"Aspects
of Operator Theory on Weighted Symmetric Fock Spaces II"

by

Hakkı Turgay
Kaptanoğlu

(Bilkent University)

Abstract: We
obtain all Dirichlet spaces of holomorphic
functions on the unit ball of  CN
as weighted symmetric Fock spaces over CN. These are reproducing
kernel Hilbert spaces on the ball with binomial or hypergeometric
kernels, and they include Bergman, Hardy, Arveson,
and Dirichlet spaces as special cases.We
consider some operator-theoretic problems related to the shift operators on
these spaces. We pick out the analytic Hilbert modules from among these spaces.We obtain von Neumann
inequalities with respect to all Dirichlet spaces,
which give upper bounds on the norms of polynomials of row contractions on
arbitrary Hilbert spaces. We prove that the C* -algebras generated by the shift operators on these
spaces, the Toeplitz algebras, fit in exact sequences
that are in the same Ext class, which allows us to compute the K-theory groups
of the Toeplitz algebras. Several other results
related to subnormality or Fredholm
properties of the shift operators can be presented if time permits. Radial
differential operators are prominent throughout.

Tea and cookies will be served before the
seminar.

Date:
Thursday, March 22, 2012

Time: 14.00 – 15:00

Place: Mathematics Seminar Room,
SA-141