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

González, 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 -