Journal of Operator Theory

Volume 42, Issue 2, Fall 1999 pp. 371-377.

Bishop's property $(\beta)$ for tensor product tuples

Authors: Roland Wolff
Author institution: Fachbereich 9 -- Mathematik, Universitaet des Saarlandes, Postfach 151150, 66041 Saarbrucken, Germany

Summary: In this paper, we prove that a tensor product tuple $R=(S\otimes I, I\otimes T)$ possesses Bishop's property $(\beta)$, supposed that the commuting tuples $S$ and $T$ of Hilbert space operators have property $(\beta)$. As an application, we show that the Hardy space $H^2(\Delta^n)$ over the polydisc in $\C^n$ is quasicoherent.

Keywords: Bishop's property $(beta)$, Hardy spaces, Toeplitz operator

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