This is an announcement for the paper "$\ell_\infty$-sums and the Banach space $\ell_\infty/c_0$" by Christina Brech and Piotr Koszmider.

Abstract: We prove that the use of the Continuum Hypothesis in some results of Drewnowski and Roberts concerning the Banach space $\ell_\infty/c_0$ cannot be avoided. In particular, we prove that in the $\omega_2$-Cohen model, $\ell_\infty(c_0(\mathfrak{c}))$ does not embed isomorphically into $\ell_\infty/c_0$ where $\mathfrak{c}$ is the cardinality of the continuum. It follows that consistently $\ell_\infty/c_0$ is not isomorphically of the form $\ell_\infty(X)$ for any Banach space $X$.

Archive classification: math.FA math.LO

Submitted from: christina.brech@gmail.com

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

http://front.math.ucdavis.edu/1211.3173

or

http://arXiv.org/abs/1211.3173