ANALYSIS
SEMINAR

"Aspects
of Operator Theory on Weighted Symmetric Fock Spaces"

By

Hakkı Turgay
Kaptanoğlu

(Bilkent University)

Abstract: We
obtain all Dirichlet spaces of holomorphic
functions on the unit ball of  C
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 15, 2012

Time: 14.00 – 15:00

Place: Mathematics Seminar Room,
SA-141