Weakly null sequences with upper estimates

Daniel Freeman

Daniel Freeman

Studia Mathematica, Tome 187 (2008), p. 79-102 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that if $(v_{i})$ is a seminormalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by $(v_{i})$ , then there exists a uniform constant C ≥ 1 such that every normalized weakly null sequence in X has a subsequence that is C-dominated by $(v_{i})$ . This extends a result of Knaust and Odell, who proved this for the cases in which $(v_{i})$ is the standard basis for $ℓ_{p}$ or c₀.

Publié le : 2008-01-01

Zbl 1140.46303

EUDML-ID : urn:eudml:doc:284835

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     author = {Daniel Freeman},
     title = {Weakly null sequences with upper estimates},
     journal = {Studia Mathematica},
     volume = {187},
     year = {2008},
     pages = {79-102},
     zbl = {1140.46303},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-1-4}
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Daniel Freeman. Weakly null sequences with upper estimates. Studia Mathematica, Tome 187 (2008) pp. 79-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-1-4/