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


Authors: G. Godefroy, J. Pelant, J. H. M. Whitfield and V. Zizler
Journal: Proc. Amer. Math. Soc. 103 (1988), 1087-1093
MSC: Primary 46E99; Secondary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1988-0954988-5
MathSciNet review: 954988
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0954988-5
Keywords: Renorming, $ {C^\infty }$-norms, three space problem, injections into $ {c_0}(\Gamma )$
Article copyright: © Copyright 1988 American Mathematical Society

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