Abstract
Abstract Let X and Y be normed spaces. A linear transformation T: D(T) X ⊂ Y is Tauberian if (T“)-1(Ŷ/D(T′)⊥) ⊂ [Dtilde](T)⁁, and an F +-operator if it has a finite codimensional restriction having a continuous inverse. In the present note it is shown that the class of Tauberian operators is stable under weakly compact perturbation and that F +-operators are Tauberian. In the case when [Dtilde](T) contains no infinite dimensional reflexive subspace it follows that T is Tauberian if and only if it is an F +-operator. As an application, Banach spaces containing no infinite dimensional reflexive subspace are characterized.
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