The p-Drazin Inverse for Operator Matrix over Banach Algebras

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Chen H., Zou H., ÇALCI T., KÖSE H.

FILOMAT, vol.34, no.14, pp.4597-4605, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 14
  • Publication Date: 2020
  • Doi Number: 10.2298/fil2014597c
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.4597-4605
  • Keywords: p-Drazin inverse, operator matrix, Banach algebra
  • Ankara University Affiliated: Yes

Abstract

An element a in a Banach algebra A has p-Drazin inverse provided that there exists b is an element of comm(a) such that b = b(2)a, a(k) - a(k+1)b is an element of J(A) for some k is an element of 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.