Weakly null sequences with upper estimates
Volume 184 / 2008
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 $c_0$.
