On generalized Drazin-Riesz operators

Abdelaziz Tajmouati,M Abkari

doi:10.5269/bspm.41488

Abstract

In this paper, we investigate the classes of operators as class of generalized Drazin Riesz operators. We give some results for these classes throught localized single valued extension property (SVEP). Some applications are given.

Highlights

Which is equivalent to the fact that T = T1 ⊕ T2, where T1 is invertible and T2 is nilpotent
The concept of Drazin invertible operators has been generalized by Koliha [7]
T ∈ B(X) is generalized Drazin invertible if and only if 0 ∈/ acc(σ(T )) (acc(σ(T )) is the set of all points of accumulation of σ(T )), which is equivalent to the fact that T = T1 ⊕ T2 where T1 is invertible and T2 is quasi-nilpotent

Summary

Introduction

Let T ∈ B(X), T is said to be a Drazin invertible if there exists a positive integer k and an operator S ∈ B(X) such that: ST = T S, T k+1S = T k and S2T = S. The concept of Drazin invertible operators has been generalized by Koliha [7]. An operator T ∈ B(X) is said to admit a generalized Kato decomposition, abbreviated as GKD, if there exists a pair (M, N ) ∈ Red(T ) such that TM is Kato and TN is quasi-nilpotent. The classes gDRR12(X) is called the class of generalized Drazin-Riesz invertible, 4.

Objectives

Results

Conclusion