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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.
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 -