Weakly null sequences with upper estimates

Details Weakly null sequences with upper estimates Weakly null sequences with upper estimates

2007-05-02

arxiv.org/abs/0705.0218v1

Mathematics

Functional Analysis

21 pages

Scientific paper

We prove that if $(v_i)$ is a normalized 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 $C\geq1$ 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 $\ell_p$ or $c_0$.

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