For a countable compact metric space and a seminormalized weakly null sequence (fₙ)ₙ in C() we provide some upper bounds for the norm of the vectors in the linear span of a subsequence of (fₙ)ₙ. These bounds depend on the complexity of and also on the sequence (fₙ)ₙ itself. Moreover, we introduce the class of c₀-hierarchies. We prove that for every α < ω₁, every normalized weakly null sequence (fₙ)ₙ in and every c₀-hierarchy generated by (fₙ)ₙ, there exists β ≤ α such that a sequence of β-blocks of (fₙ)ₙ is equivalent to the usual basis of c₀.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm187-1-3,
author = {S. A. Argyros and V. Kanellopoulos},
title = {Determining c0 in C(K) spaces},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {61-93},
zbl = {1098.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm187-1-3}
}
S. A. Argyros; V. Kanellopoulos. Determining c₀ in C(𝒦) spaces. Fundamenta Mathematicae, Tome 185 (2005) pp. 61-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm187-1-3/