Banach space properties of Ciesielski-Pol’s 𝐶(𝐾) space

Godefroy, G.; Pelant, J.; Whitfield, J. H. M.; Zizler, V.

doi:10.1090/S0002-9939-1988-0954988-5

Banach space properties of Ciesielski-Pol’s $C(K)$ space
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by G. Godefroy, J. Pelant, J. H. M. Whitfield and V. Zizler

Proc. Amer. Math. Soc. 103 (1988), 1087-1093

DOI: https://doi.org/10.1090/S0002-9939-1988-0954988-5

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Abstract:

A $C(K)$ space ${X_0}$ which Ciesielski and Pol show does not continuously linearly inject into any ${c_0}(\Gamma )$ has an equivalent ${C^\infty }$-norm, is Lipschitz equivalent to a ${c_0}(\Gamma )$, and the density character of ${X_0}$ is equal to the ${w^*}$-density character of $X_0^*$.

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