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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.

Keywords: Cowen-Douglas operators, dominating sets

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