ANALYSIS
SEMINAR

"Reflexivity,
Hyperreflexivity, and Transitivity for Toeplitz Operators"

by

Marek Ptak

(University of
Agriculture, Krakow, Poland)

Abstract: The recent reﬂexivity,
transitivity and hyperreﬂexivity results for subspaces and algebras of
Toeplitz operators will be presented. We start with the classical result about
reﬂexivity and hyperreﬂexivity of analytic Toeplitz operators on
the Hardy space on the unit disc. The space of all Toeplitz operators is
transitive but 2–reﬂexive. We will study the dichotomic behavior
of subspaces of Toeplitz operators on the Hardy space. A linear space of
Toeplitz operators which is closed in the ultraweak operator topology is either
transitive or reﬂexive. No intermediate behavior is possible. This
result can be extended to the Toeplitz operators on the Hardy space on the
upper half–plane. The Toeplitz operators on the Bergman space will be
also considered. The generalized Toeplitz and the multivariable Toeplitz
operators case will be also considered.

Tea and cookies will be served after the
seminar.

Date:
Thursday, May  03, 2012

Time: 14.00 – 15:00

Place: Mathematics Seminar Room,
SA-141