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.
"(P,Q)-outer generalized inverse of block matrices in Banach algebras." Banach J. Math. Anal. 8 (1) 98 - 108, 2014. https://doi.org/10.15352/bjma/1381782090