Differentiability of the g-Drazin inverse
JJ Koliha, V Rakocevic
STUDIA MATHEMATICA | POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN | Published : 2005
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 p-Drazin inverse A 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.