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arXiv · 1207.3722

Some remarks on universality properties of $\ell_\infty / c_0$

Mikolaj Krupski·Witold Marciszewski
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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.

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Mikolaj Krupski, Witold Marciszewski. 2012-07-16. Some remarks on universality properties of $\ell_\infty / c_0$. https://doi.org/10.4064/cm128-2-4

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