1Department of Mathematics and Statistics University of Melbourne Melbourne, VIC 3010, Australia 2Faculty of Science and Mathematics Višegradska 33 18000 Niš, Serbia-Montenegro
Studia Mathematica, Tome 168 (2005) no. 3, pp. 193-201
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.
Keywords:
function real complex variable values space bounded linear operators banach space each g drazin invertible study conditions under which g drazin inverse differentiable results recover theorem due campbell differentiability drazin inverse matrix valued function result differentiation moore penrose inverse hilbert spaces
Affiliations des auteurs :
J. J. Koliha
1
;
V. Rakočević
2
1
Department of Mathematics and Statistics University of Melbourne Melbourne, VIC 3010, Australia
2
Faculty of Science and Mathematics Višegradska 33 18000 Niš, Serbia-Montenegro
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author = {J. J. Koliha and V. Rako\v{c}evi\'c},
title = {Differentiability of the $g${-Drazin} inverse},
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J. J. Koliha; V. Rakočević. Differentiability of the $g$-Drazin inverse. Studia Mathematica, Tome 168 (2005) no. 3, pp. 193-201. doi: 10.4064/sm168-3-1
