Journal of Operator Theory

Volume 72, Issue 1, Summer 2014 pp. 277-290.

Cowen-Douglas operators and dominating sets

Authors: Joerg Eschmeier

$1$ and Johannes Schmitt

$2$
Author institution:

$1$ Fachrichtung Mathematik, Universitaet des Saarlandes, Saarbruecken, D-66123, Deutschland

$2$ Fachrichtung Mathematik, ETH Zuerich, Zuerich, CH-8092, Switzerland

Summary: It is shown that each Banach space of analytic functions with continuous point evaluations on an open set

$\Omega \subset \mathbb C^d$ possesses a discrete dominating set. This result enables us to prove the existence of spanning holomorphic cross-sections for Cowen--Douglas tuples

$T = (T_1, \ldots , T_d)$ of class

$B_n(\Omega)$ , generalizing a previous result of Kehe Zhu for single Cowen--Douglas operators. As a consequence we extend representation and classification results of Zhu to the multivariate case.

DOI: http://dx.doi.org/10.7900/jot.2013jan21.1976
Keywords: Cowen-Douglas operators, dominating sets

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