The P-Drazin İnverse for Operator Matrix Over Banach Algebras

Abstract

An element a in a Banach algebra A has p-Drazin inverse provided that there exists b2 comm(a) such that b = b2a, ak ↋ ak+1b 2 J(A) for some k 2 N. In this paper, we present new conditions for a block operator matrix to have p-Drazin inverse. As applications, we prove the p-Drazin invertibility of the block operator matrix under certain spectral conditions. © 2020, University of Nis. All rights reserved.