Illinois Journal of Mathematics

Operators in Cowen-Douglas classes

Kehe Zhu

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The paper introduces a new approach to the Cowen-Douglas theory based on the notion of a spanning holomorphic cross-section. This approach is less geometric and enables one to obtain several additional results, including one about the similarity of operators in the Cowen-Douglass classes and another about the representation of these operators as the adjoint of multiplication by $z$ on certain Hilbert spaces of holomorphic functions.

Article information

Illinois J. Math., Volume 44, Issue 4 (2000), 767-783.

First available in Project Euclid: 19 October 2009

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Zentralblatt MATH identifier

Primary: 47A45: Canonical models for contractions and nonselfadjoint operators
Secondary: 30C40: Kernel functions and applications 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]


Zhu, Kehe. Operators in Cowen-Douglas classes. Illinois J. Math. 44 (2000), no. 4, 767--783. doi:10.1215/ijm/1255984691.

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