%0 Journal Article
%T Weakly null sequences with upper estimates
%A Daniel Freeman
%J Mathematics
%D 2007
%I arXiv
%X 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 $c_0$.
%U http://arxiv.org/abs/0705.0218v1