We survey a combinatorial framework for studying subsequences of a given sequence in a Banach space, with particular emphasis on weakly-null sequences. We base our presentation on the crucial notion of barrier introduced long time ago by Nash-Williams. In fact, one of the purposes of this survey is to isolate the importance of studying mappings defined on barriers as a crucial step towards solving a given problem that involves sequences in Banach spaces. We focus our study on various forms of ?partial unconditionality? present in arbitrary weakly-null sequences in Banach spaces. We give a general notion of partial unconditionality that covers most of the known cases such as, for example, Elton?s near unconditionality, convex unconditionality, and Schreier unconditionality, but we also add some new cases.
Presentamos un marco combinatorio para estudiar subsucesiones de una sucesión dada en un espacio de Banach, con particular énfasis sobre las sucesiones que son débilmente nulas. Nos centramos principalmente en varias formas de incondicionalidad, y para ello introducimos una noción abstracta de incondicionalidad parcial, que cubre la mayoría de los tipos de incondicionalidad parcial conocidos. También desarrollamos un marco combinatorio apropiado para el estudio de las subsucesiones, que trata sobre familias de conjuntos finitos de números naturales. En dicho marco la noción de barrera introducida por Nash-Williams es principal.
@article{urn:eudml:doc:41654,
title = {Partial unconditionality of weakly null sequences.},
journal = {RACSAM},
volume = {100},
year = {2006},
pages = {237-277},
mrnumber = {MR2267411},
zbl = {1111.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41654}
}
López Abad, Jordi; Todorcevic, Stevo. Partial unconditionality of weakly null sequences.. RACSAM, Tome 100 (2006) pp. 237-277. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41654/