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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Differentiability of the $g$-Drazin inverse

### Tom 168 / 2005

Studia Mathematica 168 (2005), 193-201 MSC: 47A60, 47A05, 47A10. DOI: 10.4064/sm168-3-1

#### Streszczenie

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.

#### Autorzy

• J. J. KolihaDepartment of Mathematics and Statistics
University of Melbourne
Melbourne, VIC 3010, Australia
e-mail
• V. RakočevićFaculty of Science and Mathematics