Date & Time: Tuesday, January 13, 2009, 14:30-15:30.
Venue: Ramanujan Hall

Title: On the Reflexivity and Hyperreflexivity of Toeplitz Operators

Speaker: Marek Ptak, University of Agriculture in Krakow

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 circle. The space of all Toeplitz operators is transitive but 2­reflexive. 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. The Toeplitz operators on the Bergman space will be also considered. The generalized Toeplitz and the multivariable Toeplitz operators case will be also considered.