Determining c₀ in C(𝒦) spaces

• Autorzy: S. A. Argyros , V. Kanellopoulos
• Języki publikacji: 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.

Kategorie tematyczne

• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 06A07: Combinatorics of partially ordered sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 187
• Numer: 1
• Strony: 61-93

Daty

wydano

2005

Twórcy

autor

S. A. Argyros

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

autor

V. Kanellopoulos

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

Identyfikatory

DOI

10.4064/fm187-1-3