We prove that if is not a Kunen cardinal, then there is a uniform Eberlein compact space K such that the Banach space C(K) does not embed isometrically into . We prove a similar result for isomorphic embeddings. Our arguments are minor modifications of the proofs of analogous results for Corson compacta obtained by S. Todorčević. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into , but fails to embed isometrically. As far as we know it is the first example of this kind.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-4,
author = {Miko\l aj Krupski and Witold Marciszewski},
title = {Some remarks on universality properties of $l\_[?]/c0$
},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {187-195},
zbl = {1267.46031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-4}
}
Mikołaj Krupski; Witold Marciszewski. Some remarks on universality properties of $ℓ_∞/c₀$
. Colloquium Mathematicae, Tome 126 (2012) pp. 187-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-4/