On Tauberian and co-Tauberian operators

Autores: Vladimir P. Fonf , S. Dutta
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 21, Nº 1, 2006, págs. 27-40
Idioma: inglés
Títulos paralelos:
- Sobre los operadores tauberianos y cotauberianos
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Resumen
- 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 nonisomorphic 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*