Weakly null sequences with upper estimates
Studia Mathematica, Tome 184 (2008) no. 1, pp. 79-102
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $c_0$.
Keywords:
prove seminormalized basic sequence banach space every normalized weakly null sequence has subsequence dominated there exists uniform constant geq every normalized weakly null sequence has subsequence c dominated extends result knaust odell who proved cases which standard basis ell
Affiliations des auteurs :
Daniel Freeman 1
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author = {Daniel Freeman},
title = {Weakly null sequences with upper estimates},
journal = {Studia Mathematica},
pages = {79--102},
publisher = {mathdoc},
volume = {184},
number = {1},
year = {2008},
doi = {10.4064/sm184-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm184-1-4/}
}
Daniel Freeman. Weakly null sequences with upper estimates. Studia Mathematica, Tome 184 (2008) no. 1, pp. 79-102. doi: 10.4064/sm184-1-4
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