Ordinal indices and Ramsey dichotomies measuring c₀-content and semibounded completeness

• Autorzy: Vassiliki Farmaki
• Języki publikacji: EN

Abstrakty

EN

We study the c₀-content of a seminormalized basic sequence (χₙ) in a Banach space, by the use of ordinal indices (taking values up to ω₁) that determine dichotomies at every ordinal stage, based on the Ramsey-type principle for every countable ordinal, obtained earlier by the author. We introduce two such indices, the c₀-index $ξ^{(χₙ)}₀$ and the semibounded completeness index $ξ^{(χₙ)}_b$, and we examine their relationship. The countable ordinal values that these indices can take are always of the form $ω^{ζ}$. These results extend, to the countable ordinal level, an earlier result by Odell, which was stated only for the limiting case of the first uncountable ordinal.

Kategorie tematyczne

• 46B45: Banach sequence spaces
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 172
• Numer: 2
• Strony: 153-179

Daty

wydano

2002

Twórcy

autor

Vassiliki Farmaki

• Department of Mathematics, University of Athens, Panepistimiopolis, 15784 Athens, Greece

Identyfikatory

DOI

10.4064/fm172-2-4