# On Tauberian and co-Tauberian operators.

Sudipta Dutta; Vladimir P. Fonf

Extracta Mathematicae (2006)

- Volume: 21, Issue: 1, page 27-39
- ISSN: 0213-8743

## Access Full Article

top## Abstract

top## How to cite

topDutta, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.