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

### Tom 217 / 2013

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

#### Streszczenie

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 $1 \leq n, k <\omega$.

#### Autorzy

• 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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