How far is $C(\omega )$ from the other $C(K)$ spaces?

Leandro Candido ¹   ; Elói Medina Galego ²

¹ Department of Mathematics University of São Paulo São Paulo, Brazil 05508-090
² Department of Mathematics University of Sõ Paulo São Paulo, Brazil 05508-090

Studia Mathematica, Tome 217 (2013) no. 2, pp. 123-138

Résumé

Let us denote by $C(\alpha )$ the classical Banach space $C(K)$ when $K$ is the interval of ordinals $ [1, \alpha ]$ 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 $C(\omega )$ 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 $d(C(\omega ), C(\omega ^{n} k))$ such that $U(n,k)-L(n, k)2$ for all $1 \leq n, k \omega $.

Détail

DOI : 10.4064/sm217-2-2

Keywords: denote alpha classical banach space interval ordinals alpha endowed order topology present paper answer bessaga czy ski question providing tight bounds banach mazur distance between omega other space which isomorphic precisely obtain lower bounds upper bounds omega omega l leq omega