Differentiability of the $g$-Drazin inverse
Volume 168 / 2005
Studia Mathematica 168 (2005), 193-201
MSC: 47A60, 47A05, 47A10.
DOI: 10.4064/sm168-3-1
Abstract
If $A(z)$ is a function of a real or complex variable with values in the space $B(X)$ of all bounded linear operators on a Banach space $X$ with each $A(z)$ $g$-Drazin invertible, we study conditions under which the $g$-Drazin inverse ${A}^{\sf D}(z)$ is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a matrix-valued function and a result on differentiation of the Moore–Penrose inverse in Hilbert spaces.
