Full Length Research Paper
Abstract
In this paper, we investigate properties of with closed range satisfying the operator equations
In particular, we investigate the invertibility of
with closed range where the Moore-Penrose inverse of T turns out to be the usual inverse of T under some classes of operators. We also deduce the Moore-Penrose inverse of a perturbed linear operator
with closed range where
such that
has closed ranges and
satisfying some given conditions. The relation between the ranges and null spaces of these operators is also shown.
Key words: Moore-Penrose inverse, perturbed linear operator, invertibility of operators.
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