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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2005 | 187 | 1 | 61-93

## Determining c₀ in C(𝒦) spaces

EN

### Abstrakty

EN
For a countable compact metric space 𝒦 and a seminormalized weakly null sequence (fₙ)ₙ in C(𝒦) 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 𝒦 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 𝓗 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.

61-93

wydano
2005

### Twórcy

autor
• Department of Mathematics, National Technical University of Athens, Athens 15780, Greece
autor
• Department of Mathematics, National Technical University of Athens, Athens 15780, Greece