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## On Banach spaces $C(K)$ isomorphic to $c_0({\mit\Gamma })$

### Tom 156 / 2003

Studia Mathematica 156 (2003), 295-302 MSC: Primary 46B03, 46E15. DOI: 10.4064/sm156-3-6

#### Streszczenie

We give a characterization of compact spaces $K$ such that the Banach space $C(K)$ is isomorphic to the space $c_0({\mit\Gamma })$ for some set ${\mit\Gamma }$. As an application we show that there exists an Eberlein compact space $K$ of weight $\omega _\omega$ and with the third derived set $K^{(3)}$ empty such that the space $C(K)$ is not isomorphic to any $c_0({\mit\Gamma })$. For this compactum $K$, the spaces $C(K)$ and $c_0(\omega _\omega )$ are examples of weakly compactly generated (WCG) Banach spaces which are Lipschitz isomorphic but not isomorphic.

#### Autorzy

• Witold MarciszewskiInstitute of Mathematics
University of Warsaw
Banacha 2
02-097 Warszawa, Poland
e-mail

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