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 and the semibounded completeness index , and we examine their relationship. The countable ordinal values that these indices can take are always of the form . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-2-4,
author = {Vassiliki Farmaki},
title = {Ordinal indices and Ramsey dichotomies measuring c0-content and semibounded completeness},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {153-179},
zbl = {1005.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-2-4}
}
Vassiliki Farmaki. Ordinal indices and Ramsey dichotomies measuring c₀-content and semibounded completeness. Fundamenta Mathematicae, Tome 173 (2002) pp. 153-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-2-4/