Article

On deriving the generalized Drazin inverse of block matrices in a Banach algebra

Published in: Quaestiones Mathematicae
Volume 39 , issue 4 , 2016 , pages: 511–521

DOI: 10.2989/16073606.2015.1096861

Author(s): Dijana Mosić Faculty of Sciences and Mathematics, University of Niš, Serbia

Keywords: 46H05 , 47A05 , 15A09 , 46H05 , 47A05 , 15A09

Abstract

This paper is devoted to the generalized Drazin inverse of a block matrix

in a Banach algebra A, under specific conditions. We focus on deriving formulae for the generalized Drazin inverse of x in terms of the generalized Drazin inverses of the elements a, a^π bc, a² a^d +aa^d bca^d and the generalized Schur complement s=d−ca^d b.

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