On Corson compacta and embeddings of 𝐶(𝐾) spaces

Marciszewski, Witold; Plebanek, Grzegorz

doi:10.1090/S0002-9939-2010-10403-3

On Corson compacta and embeddings of $C(K)$ spaces
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by Witold Marciszewski and Grzegorz Plebanek

Proc. Amer. Math. Soc. 138 (2010), 4281-4289

DOI: https://doi.org/10.1090/S0002-9939-2010-10403-3

Published electronically: May 17, 2010

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Abstract:

We investigate properties of those compact spaces $K$ for which the Banach space $C(K)$ can be isomorphically embedded into a space $C(L)$, where $L$ is Corson compact. We show that in such a case $K$ must be Corson compact provided $K$ has some additional measure–theoretic property. The result is applicable to Rosenthal compacta and several other classes of compact spaces $K$.

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