# Representation of operators with martingales and the Radon-Nikodým property.

Manuel González; Antonio Martínez-Abejón; Javier Pello-García

Extracta Mathematicae (2004)

- Volume: 19, Issue: 1, page 135-140
- ISSN: 0213-8743

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topGonzález, Manuel, Martínez-Abejón, Antonio, and Pello-García, Javier. "Representation of operators with martingales and the Radon-Nikodým property.." Extracta Mathematicae 19.1 (2004): 135-140. <http://eudml.org/doc/38678>.

@article{González2004,

abstract = {The Radon-Nikodým property was introduced to describe those Banach spaces X for which all operators acting between L1 and X have a representation function. These spaces can be characterized in terms of martingales, as those spaces in which every uniformly bounded martingale converges. In the present work we study some classes of operators defined upon their behaviour with respect to the convergence of such martingales. We prove that an operator preserves the non-convergence of uniformly bounded martingales if and only if all its compact perturbations have Asplund cokernel.},

author = {González, Manuel, Martínez-Abejón, Antonio, Pello-García, Javier},

journal = {Extracta Mathematicae},

keywords = {Espacios de Banach; Propiedad de Radon-Nikodym; Operadores lineales; Teoría de perturbación; Convergencia de martingalas; martingales; Radon-Nikodym property},

language = {eng},

number = {1},

pages = {135-140},

title = {Representation of operators with martingales and the Radon-Nikodým property.},

url = {http://eudml.org/doc/38678},

volume = {19},

year = {2004},

}

TY - JOUR

AU - González, Manuel

AU - Martínez-Abejón, Antonio

AU - Pello-García, Javier

TI - Representation of operators with martingales and the Radon-Nikodým property.

JO - Extracta Mathematicae

PY - 2004

VL - 19

IS - 1

SP - 135

EP - 140

AB - The Radon-Nikodým property was introduced to describe those Banach spaces X for which all operators acting between L1 and X have a representation function. These spaces can be characterized in terms of martingales, as those spaces in which every uniformly bounded martingale converges. In the present work we study some classes of operators defined upon their behaviour with respect to the convergence of such martingales. We prove that an operator preserves the non-convergence of uniformly bounded martingales if and only if all its compact perturbations have Asplund cokernel.

LA - eng

KW - Espacios de Banach; Propiedad de Radon-Nikodym; Operadores lineales; Teoría de perturbación; Convergencia de martingalas; martingales; Radon-Nikodym property

UR - http://eudml.org/doc/38678

ER -

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