How far is C(ω) from the other C(K) spaces?

Leandro Candido, and Elói Medina Galego. "How far is C(ω) from the other C(K) spaces?." Studia Mathematica 217.2 (2013): 123-138. <http://eudml.org/doc/285763>.

@article{LeandroCandido2013,
abstract = {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.},
author = {Leandro Candido, Elói Medina Galego},
journal = {Studia Mathematica},
keywords = { space; space; Banach-Mazur distance},
language = {eng},
number = {2},
pages = {123-138},
title = {How far is C(ω) from the other C(K) spaces?},
url = {http://eudml.org/doc/285763},
volume = {217},
year = {2013},
}

TY - JOUR
AU - Leandro Candido
AU - Elói Medina Galego
TI - How far is C(ω) from the other C(K) spaces?
JO - Studia Mathematica
PY - 2013
VL - 217
IS - 2
SP - 123
EP - 138
AB - 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.
LA - eng
KW - space; space; Banach-Mazur distance
UR - http://eudml.org/doc/285763
ER -