Determining c₀ in C(𝒦) spaces

S. A. Argyros, and V. Kanellopoulos. "Determining c₀ in C(𝒦) spaces." Fundamenta Mathematicae 187.1 (2005): 61-93. <http://eudml.org/doc/283132>.

@article{S2005,
abstract = {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 $C(ω^\{ω^\{α\}\})$ 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.},
author = {S. A. Argyros, V. Kanellopoulos},
journal = {Fundamenta Mathematicae},
keywords = {-sequences; Schreier families; spaces},
language = {eng},
number = {1},
pages = {61-93},
title = {Determining c₀ in C(𝒦) spaces},
url = {http://eudml.org/doc/283132},
volume = {187},
year = {2005},
}

TY - JOUR
AU - S. A. Argyros
AU - V. Kanellopoulos
TI - Determining c₀ in C(𝒦) spaces
JO - Fundamenta Mathematicae
PY - 2005
VL - 187
IS - 1
SP - 61
EP - 93
AB - 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 $C(ω^{ω^{α}})$ 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.
LA - eng
KW - -sequences; Schreier families; spaces
UR - http://eudml.org/doc/283132
ER -