English

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

Functional Analysis 2018-12-12 v1

Abstract

We prove that if continuum is not a Kunen cardinal, then there is a uniform Eberlein compact space KK such that the Banach space C(K)C(K) does not embed isometrically into /c0\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 /c0\ell_\infty/c_0, but fails to embed isometrically. As far as we know it is the first example of this kind.

Keywords

Cite

@article{arxiv.1207.3722,
  title  = {Some remarks on universality properties of $\ell_\infty / c_0$},
  author = {Mikolaj Krupski and Witold Marciszewski},
  journal= {arXiv preprint arXiv:1207.3722},
  year   = {2018}
}