Geodesic
Differentiability of the $g$-Drazin inverse
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
Studia Mathematica, Tome 168 (2005) no. 3, pp. 193-201 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm168-3-1
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

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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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

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