On Tauberian and co-Tauberian operators.

Dutta, Sudipta, and Fonf, Vladimir P.. "On Tauberian and co-Tauberian operators.." Extracta Mathematicae 21.1 (2006): 27-39. <http://eudml.org/doc/41847>.

@article{Dutta2006,
abstract = {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*.},
author = {Dutta, Sudipta, Fonf, Vladimir P.},
journal = {Extracta Mathematicae},
keywords = {Geometría y estructura de espacios de Banach; Operadores tauberianos; Inmersiones; Tauberian operator; co-Tauberian operator; -embedded spaces; -embedded spaces; property },
language = {eng},
number = {1},
pages = {27-39},
title = {On Tauberian and co-Tauberian operators.},
url = {http://eudml.org/doc/41847},
volume = {21},
year = {2006},
}

TY - JOUR
AU - Dutta, Sudipta
AU - Fonf, Vladimir P.
TI - On Tauberian and co-Tauberian operators.
JO - Extracta Mathematicae
PY - 2006
VL - 21
IS - 1
SP - 27
EP - 39
AB - 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*.
LA - eng
KW - Geometría y estructura de espacios de Banach; Operadores tauberianos; Inmersiones; Tauberian operator; co-Tauberian operator; -embedded spaces; -embedded spaces; property 
UR - http://eudml.org/doc/41847
ER -