(P,Q)-outer generalized inverse of block matrices in Banach algebras

Abstract

We investigate additive results for $(p,q)$-outer generalized inverse of elements in Banach algebra, along with the representation of this inverse in a block matrix in the Banachiewicz--Schur form. Additionally, we investigate the $(p,q)$-pseudospectrum and $(p,q)$-condition spectrum of a block matrix $(a,0,0,b)$ in a Banach algebra.