This is an announcement for the paper "Weakly null sequences with upper estimates" by Daniel Freeman.

Abstract: 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 $c_0$.

Archive classification: math.FA

Mathematics Subject Classification: 46B20; 46B03, 46B10

Remarks: 21 pages

The source file(s), FreemanUpEst.tex, is(are) stored in gzipped form as 0705.0218.gz with size 20kb. The corresponding postcript file has gzipped size 146kb.

Submitted from: freeman@math.tamu.edu

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