J. Aust. Math. Soc.
82 (2007), 163181

The weighted gDrazin inverse for operators

Alegra Dajic
Department of Mathematics and Statistics
The University of Melbourne
VIC 3010
Australia
a.dajic@ms.unimelb.edu.au





Abstract

The paper introduces and studies the weighted
gDrazin inverse for bounded linear
operators between Banach spaces, extending the
concept of the weighted Drazin inverse
of Rakocevic and Wei (Linear Algebra Appl.
350 (2002), 25–39) and of Cline and Greville
(Linear Algebra Appl. 29 (1980),
53–62). We use the Mbekhta decomposition to
study the structure of an operator possessing the
weighted gDrazin inverse, give an
operator matrix representation for the inverse,
and study its continuity. An open problem of
Rakocevic and Wei is solved.

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