## Illinois Journal of Mathematics

### Operators in Cowen-Douglas classes

Kehe Zhu

#### Abstract

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

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

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255984691

Digital Object Identifier
doi:10.1215/ijm/1255984691

Mathematical Reviews number (MathSciNet)
MR1804320

Zentralblatt MATH identifier
0972.47006

#### Citation

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