Weakly null sequences with upper estimates

Volume 184 / 2008

Daniel Freeman Studia Mathematica 184 (2008), 79-102 MSC: Primary 46B20; Secondary 46B03, 46B45. DOI: 10.4064/sm184-1-4

Abstract

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 $C\geq 1$ 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 $\ell _p$ or $c_0$.

Authors

  • Daniel FreemanDepartment of Mathematics
    Texas A&M University
    College Station, TX 77843-3368, U.S.A.
    e-mail

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