Generalized Drazin-Meromorphic Invertible Operators and Browder's Type Theorems

TL;DR

This paper characterizes generalized Drazin-Riesz and meromorphic invertibility of bounded operators and explores generalized Browder's theorems using spectral interior points.

Contribution

It provides necessary and sufficient conditions for generalized Drazin-Riesz and meromorphic invertibility and studies generalized Browder's theorems via spectral interior points.

Findings

Characterization of generalized Drazin-Riesz invertibility

Conditions for generalized Drazin-meromorphic invertibility

Analysis of generalized Browder's theorems using spectral interior points

Abstract

In this paper we give necessary and sufficient conditions for a bounded linear operator $T$ to be generalized Drazin-Riesz invertible or generalized Drazin-meromorphic invertible. Also, we study generalized Browder's theorem and generalized a-Browder's theorem by means of set of interior points of various parts of spectrum of $T$.