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.

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