Journal of Operator Theory

Volume 49, Issue 2, Spring 2003 pp. 407-420.

Property

$(\beta)_{\cal E}$ for Toeplitz operators with

$H^\infty$ -symbol

Authors: Sebastian Sandberg
Author institution: Department of Mathematics, Chalmers University of Technology and University of Goeteborg, SE-412 96 Goeteborg, Sweden

Summary: Suppose that

$g$ is a tuple of bounded holomorphic functions on a strictly pseudoconvex domain

$D$ in

$\C^m$ with smooth boundary. Viewed as a tuple of operators on the Hardy space

$H^p(D)$ ,

$1\leq p<\infty$ ,

$g$ is shown to have property

$(\beta)_{\cal E}$ and therefore

$g$ possess Bishop's property

$(\beta)$ . In the case

$m=1$ it is proved that the same result also holds when

$p=\infty$ .

Contents Full-Text PDF