Journal of Operator Theory

Volume 45, Issue 2, Spring 2001 pp. 233-249.

Representations of $H^{\infty}({\bbb D}^N)$

Authors: George R. Exner (1), Young Soo Jo (2), and Il Bong Jung (3)
Author institution: (1) Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA
(2) Department of Mathematics, College of Natural Sciences, Kyemyung University, Taegu, 704--200, Korea
(3) Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu, 702--701, Korea

Summary: We consider dual operator algebra properties of the range of a representation from $H^\infty(\D^N)$ into the bounded linear operators on Hilbert space. If the representation is of $C_{00}$ type, properties ($\A_{\aleph_0}$) and $X_{0, 1/M}$ coincide, where $M$ is the bound of the representation. Specializing to the representation induced by a pair of commuting contractions, we obtain an improved result.

Keywords: Dual operator algebras, representation, dilation, compression, polynom ially bounded operator, commuting contractions

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