Differentiability of the $g$-Drazin inverse

Volume 168 / 2005

J. J. Koliha, V. Rakočević 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.

Authors

  • J. J. KolihaDepartment of Mathematics and Statistics
    University of Melbourne
    Melbourne, VIC 3010, Australia
    e-mail
  • V. RakočevićFaculty of Science and Mathematics
    Višegradska 33
    18000 Niš, Serbia-Montenegro
    e-mail

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