On Banach spaces $C(K)$ isomorphic to $c_0({\mit\Gamma })$
Volume 156 / 2003
Studia Mathematica 156 (2003), 295-302
MSC: Primary 46B03, 46E15.
DOI: 10.4064/sm156-3-6
Abstract
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.
