Weakly null sequences with upper estimates
Daniel Freeman (2008)
Studia Mathematica
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We prove that if 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 , 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 . This extends a result of Knaust and Odell, who proved this for the cases in which is the standard basis for or c₀.