On Tauberian and co-Tauberian operators.
We show that a Banach space X has an infinite dimensional reflexive subspace (quotient) if and only if there exist a Banach space Z and a non-isomorphic one-to-one (dense range) Tauberian (co-Tauberian) operator form X to Z (Z to X). We also give necessary and sufficient condition for the existence of a Tauberian operator from a separable Banach space to c which in turn generalizes a result of Johnson and Rosenthal. Another application of our result shows that if X** is separable, then there exists...