# Partial unconditionality of weakly null sequences.

Jordi López Abad; Stevo Todorcevic

RACSAM (2006)

- Volume: 100, Issue: 1-2, page 237-277
- ISSN: 1578-7303

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topLópez Abad, Jordi, and Todorcevic, Stevo. "Partial unconditionality of weakly null sequences.." RACSAM 100.1-2 (2006): 237-277. <http://eudml.org/doc/41654>.

@article{LópezAbad2006,

abstract = {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.},

author = {López Abad, Jordi, Todorcevic, Stevo},

journal = {RACSAM},

keywords = {weakly-null sequences; barrier; partial unconditionality},

language = {eng},

number = {1-2},

pages = {237-277},

title = {Partial unconditionality of weakly null sequences.},

url = {http://eudml.org/doc/41654},

volume = {100},

year = {2006},

}

TY - JOUR

AU - López Abad, Jordi

AU - Todorcevic, Stevo

TI - Partial unconditionality of weakly null sequences.

JO - RACSAM

PY - 2006

VL - 100

IS - 1-2

SP - 237

EP - 277

AB - 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.

LA - eng

KW - weakly-null sequences; barrier; partial unconditionality

UR - http://eudml.org/doc/41654

ER -

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