Note on distortion and Bourgain ℓ₁-index

Anna Maria Pelczar

Studia Mathematica, Tome 192 (2009), p. 147-161 / Harvested from The Polish Digital Mathematics Library

Résumé

Relations between different notions measuring proximity to ℓ₁ and distortability of a Banach space are studied. The main result states that a Banach space all of whose subspaces have Bourgain ℓ₁-index greater than $ω^{α}$ , α < ω₁, contains either an arbitrarily distortable subspace or an $ℓ ₁^{α}$ -asymptotic subspace.

Publié le : 2009-01-01

Zbl 1167.46006

EUDML-ID : urn:eudml:doc:284632

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     author = {Anna Maria Pelczar},
     title = {Note on distortion and Bourgain l1-index},
     journal = {Studia Mathematica},
     volume = {192},
     year = {2009},
     pages = {147-161},
     zbl = {1167.46006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-2-4}
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Anna Maria Pelczar. Note on distortion and Bourgain ℓ₁-index. Studia Mathematica, Tome 192 (2009) pp. 147-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-2-4/