Coperturbation function and lower semi-Browder multivalued linear operators

Abstract

In this article, we investigate the perturbation theory of lower semi-Browder and Browder linear relations. Our approach is based on the concept of a coperturbation function for linear relations in order to establish some perturbation theorems and deduce the stability under strictly cosingular operator perturbations. Furthermore, we apply the obtained results to study the invariance and the characterization of Browder's essential defect spectrum and Browder's essential spectrum.

Keywords:

• Browder and semi-Browder linear relations
• coperturbation function
• Browder's essential defect spectrum
• Browder's essential spectrum

AMS Subject Classification:

• 47A 06

Acknowledgements

The work of T. Alvarez was supported by DGI (Spain) Grant MTM 2010-20190.