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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 $p=\infty$.

Keywords:  Bishop's property $(\beta)$, Hardy space, $H^p$-corona problem

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