This is an announcement for the paper "Some remarks on universality properties of $\ell_\infty / c_0$" by Mikolaj Krupski and Witold Marciszewski.

Abstract: We prove that if continuum 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 $\ell_\infty/c_0$. We prove a similar result for isomorphic embeddings. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $\ell_\infty/c_0$, but fails to embed isometrically. As far as we know it is the first example of this kind.

Archive classification: math.FA

Mathematics Subject Classification: Primary 46B26, 46E15, Secondary 03E75

Submitted from: krupski@impan.pl

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.3722

or

http://arXiv.org/abs/1207.3722