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 c0 which in turn generalizes a result of Johnson and Rosenthal. Another application of our result shows that if X** is separable, then there exists a renorming of X for which, X is essentially the only subspace contained in the set of norm attaining functionals on X*.
@article{urn:eudml:doc:41847,
title = {On Tauberian and co-Tauberian operators.},
journal = {Extracta Mathematicae},
volume = {21},
year = {2006},
pages = {27-39},
zbl = {1112.46006},
mrnumber = {MR2258344},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41847}
}
Dutta, Sudipta; Fonf, Vladimir P. On Tauberian and co-Tauberian operators.. Extracta Mathematicae, Tome 21 (2006) pp. 27-39. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41847/