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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