Abstract of a paper by Christina Brech and Piotr Koszmider
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
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alspach@math.okstate.edu