Weakly null sequences with upper estimates

Daniel Freeman. "Weakly null sequences with upper estimates." Studia Mathematica 184.1 (2008): 79-102. <http://eudml.org/doc/284835>.

@article{DanielFreeman2008,
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 ≥ 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 $ℓ_\{p\}$ or c₀.},
author = {Daniel Freeman},
journal = {Studia Mathematica},
keywords = {upper estimates; uniform estimates; weakly null sequences},
language = {eng},
number = {1},
pages = {79-102},
title = {Weakly null sequences with upper estimates},
url = {http://eudml.org/doc/284835},
volume = {184},
year = {2008},
}

TY - JOUR
AU - Daniel Freeman
TI - Weakly null sequences with upper estimates
JO - Studia Mathematica
PY - 2008
VL - 184
IS - 1
SP - 79
EP - 102
AB - 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 ≥ 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 $ℓ_{p}$ or c₀.
LA - eng
KW - upper estimates; uniform estimates; weakly null sequences
UR - http://eudml.org/doc/284835
ER -