On the hyperreflexivity and subspaces of Toeplitz operators on Bergman space
by
Marek Ptak
Krakow, Poland

For any B in \bold B(H), let dist(B, \Cal M) denote the usual distance from B to \Cal M in \bold B(H), and let

\alpha(B, \Cal M)= sup {||Q \perp BP||: P, Q projections with Q \perp \Cal M P=(0)}.

The linear space \Cal M is called hyperreflexive if there is a constant C > 0 such that dist(B.\Cal M) <= C \alpha(B, \Cal M) for every B in \boldB(H).

It is shown that the space of all Toeplitz operators with a bounded harmonic symbol acting on the Bergman space of the disc is hyperreflexive.

As a main tool a natural L^\infty functional calculus for an absolutely continuous contraction is investigated. The main step shows that if the functional calculus is isometric on H^\infty, then it is isometric on all of L^\infty.

This is a joint work with John B. Conway.

Date received: May 18, 2001

Copyright © 2001 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 # cagt-47.