ON THE PERTURBATION OF UNBOUNDED LINEAR-OPERATORS WITH TOPOLOGICALLY COMPLEMENTED RANGES

Let X and Y be normed spaces and let T: D(T) ⊂ X → Y be a linear transformation having a finite codimensional restriction with a continuous inverse (equivalently, let T- be a φ--operator; for example, if T is bounded below). Suppose that R(T) or R(T) is topologically complemented in Y. Conditions are obtained under which R(T+S) (resp. R(T + S)) is topologically complemented whenever S belongs to the class of precompact operators, or to some wider class. © 1990.