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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-3-1,
author = {J. J. Koliha and V. Rako\v cevi\'c},
title = {Differentiability of the g-Drazin inverse},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {193-201},
zbl = {1071.47019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-3-1}
}
J. J. Koliha; V. Rakočević. Differentiability of the g-Drazin inverse. Studia Mathematica, Tome 166 (2005) pp. 193-201. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-3-1/