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Continuity of the Drazin inverse II

J. KolihaV. Rakočević — 1998

Studia Mathematica

We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.

Measure of noncompactness of linear operators between spaces of sequences that are ( N ¯ , q ) summable or bounded

Eberhard MalkowskyV. Rakočević — 2001

Czechoslovak Mathematical Journal

In this paper we investigate linear operators between arbitrary BK spaces X and spaces Y of sequences that are ( N ¯ , q ) summable or bounded. We give necessary and sufficient conditions for infinite matrices A to map X into Y . Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for A to be a compact operator.

Differentiability of the g-Drazin inverse

J. J. KolihaV. Rakočević — 2005

Studia Mathematica

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 ( 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.

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