Let us denote by C(α) the classical Banach space C(K) when K is the interval of ordinals [1,α] endowed with the order topology. In the present paper, we give an answer to a 1960 Bessaga and Pełczyński question by providing tight bounds for the Banach-Mazur distance between C(ω) and any other C(K) space which is isomorphic to it. More precisely, we obtain lower bounds L(n,k) and upper bounds U(n,k) on d(C(ω),C(ωⁿk)) such that U(n,k) - L(n,k) < 2 for all 1 ≤ n, k < ω.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-2-2,
author = {Leandro Candido and El\'oi Medina Galego},
title = {How far is C($\omega$) from the other C(K) spaces?},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {123-138},
zbl = {1288.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-2-2}
}
Leandro Candido; Elói Medina Galego. How far is C(ω) from the other C(K) spaces?. Studia Mathematica, Tome 215 (2013) pp. 123-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-2-2/