Browder-type theorems for generalized Drazin invertible operators and applications

Abstract

In this paper, we investigate the connections between certain spectra arising from Fredholm theory of a generalized Drazin invertible bounded linear operator and those of its generalized Drazin inverse. Furthermore, we analyze the transfer of Browder’s theorem and its generalized form from such an operator to its corresponding generalized Drazin inverse. Applications to left, right, and multiplication operators are also presented.