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arXiv · 1902.07783

Twisted sums of $c_0$ and $C(K)$-spaces: A solution to the CCKY problem

Antonio Avilés·Witold Marciszewski·Grzegorz Plebanek
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Abstract

We consider the class of Banach space $Y$ for which $c_0$ admits a nontrivial twisted sum with $Y$. We present a characterization of such space $Y$ in terms of properties of the $weak^\ast$ topology on $Y^\ast$. We prove that under the continuum hypothesis $c_0$ has a nontrivial twisted sum with every space of the form $Y=C(K)$, where $K$ is compact and not metrizable. This gives a consistent positive solution to a problem posed by Cabello, Castillo, Kalton and Yost.

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Antonio Avilés, Witold Marciszewski, Grzegorz Plebanek. 2019-02-20. Twisted sums of $c_0$ and $C(K)$-spaces: A solution to the CCKY problem. https://arxiv.org/abs/1902.07783

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