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

Vassiliki Farmaki. "Ordinal indices and Ramsey dichotomies measuring c₀-content and semibounded completeness." Fundamenta Mathematicae 172.2 (2002): 153-179. <http://eudml.org/doc/282705>.

@article{VassilikiFarmaki2002,
abstract = {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.},
author = {Vassiliki Farmaki},
journal = {Fundamenta Mathematicae},
keywords = {Ramsey-type principle; Schreier system; -index; semi-bounded completeness index; seminormalized basic sequence},
language = {eng},
number = {2},
pages = {153-179},
title = {Ordinal indices and Ramsey dichotomies measuring c₀-content and semibounded completeness},
url = {http://eudml.org/doc/282705},
volume = {172},
year = {2002},
}

TY - JOUR
AU - Vassiliki Farmaki
TI - Ordinal indices and Ramsey dichotomies measuring c₀-content and semibounded completeness
JO - Fundamenta Mathematicae
PY - 2002
VL - 172
IS - 2
SP - 153
EP - 179
AB - 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.
LA - eng
KW - Ramsey-type principle; Schreier system; -index; semi-bounded completeness index; seminormalized basic sequence
UR - http://eudml.org/doc/282705
ER -