Original Articles

F₊-OPERATORS ARE TAUBERIAN

Published in: Quaestiones Mathematicae
Volume 16 , issue 2 , 1993 , pages: 129–132

DOI: 10.1080/16073606.1993.9631723

Author(s): R.W. Cross Department of Mathematics,

Keywords: 47A05

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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