Geodesic
On Banach spaces $C(K)$ isomorphic to $c_0({\mit\Gamma })$
Witold Marciszewski1
1 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Studia Mathematica, Tome 156 (2003) no. 3, pp. 295-302

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm156-3-6
Keywords: characterization compact spaces banach space isomorphic space mit gamma set mit gamma application there exists eberlein compact space weight omega omega third derived set empty space isomorphic mit gamma compactum spaces omega omega examples weakly compactly generated wcg banach spaces which lipschitz isomorphic isomorphic

Witold Marciszewski 1

1 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
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Witold Marciszewski. On Banach spaces $C(K)$ isomorphic to $c_0({\mit\Gamma })$. Studia Mathematica, Tome 156 (2003) no. 3, pp. 295-302. doi: 10.4064/sm156-3-6

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