Toeplitz Operators: Dichotomy of Reflexivity and Transitivity
by
Marek Ptak
University of Krakow
Coauthors: Edward A. Azoff

Let S be a linear manifold of bounded Hilbert space operators. An operator A belongs to ref S, the reflexive closure of S, if Af belongs to the closure of S f for each vector f in the underlying Hilbert space. Two extreme possibilities are (1) S is reflexive in the sense that ref S = S, and (2) S is transitive in the sense that ref S includes all bounded operators on the underlying space.

We show that every linear space B of Toeplitz operators which is closed in the ultraweak operator topology is either transitive or reflexive. No intermediate behavior is possible.

Date received: May 7, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacw-65.