The stability of bounded non-semi-Fredholm operators under compact perturbations was studied by R. Bouldin [1] in the case of Hilbert spaces, and subsequently by M. Gonzalez and V.M. Onieva [10] in the Banach spce case. This problem was considered in the setting of closed operators between operator ranges by L.E. Labuechaene [12]. The aim of this paper is to consider this problem in the much more general setting of unbounded linear operators between nod linear spaces. Instead of considering the classical classes ofnormally solvable, φ−and φb+operators, we consider the related classes ofrelatively open, F−and F+operators respectively. We effect a characterisation of the non-Semi-Fredholm type operators in term of certain disjoint subeta of the non-nornrally solvable type operators, as well as generalising a result of M.A. Goldman [9].
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