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

Volume 217 / 2013

Leandro Candido, Elói Medina Galego Studia Mathematica 217 (2013), 123-138 MSC: Primary 46B03, 46E15; Secondary 46B25. DOI: 10.4064/sm217-2-2

Abstract

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 $.

Authors

  • Leandro CandidoDepartment of Mathematics
    University of São Paulo
    São Paulo, Brazil 05508-090
    e-mail
  • Elói Medina GalegoDepartment of Mathematics
    University of Sõ Paulo
    São Paulo, Brazil 05508-090
    e-mail

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