Cyclicity of Cowen-Douglas tuples

TL;DR

This paper proves that all Cowen-Douglas tuples are cyclic by utilizing complex geometric methods related to holomorphic vector bundles, advancing the understanding of their operator-theoretic properties.

Contribution

It establishes that every Cowen-Douglas tuple is cyclic, providing a new geometric perspective on their structure and properties.

Findings

All Cowen-Douglas tuples are cyclic.

Utilizes complex geometry of holomorphic vector bundles.

Bridges operator theory with complex geometry.

Abstract

The study of Cowen-Douglas operators involves not only operator-theoretic tools but also complex geometry on holomorphic vector bundles. By leveraging the properties of holomorphic vector bundles, this paper investigates the cyclicity of Cowen-Douglas tuples and demonstrates conclusively that every such tuple is cyclic.