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

Antonio Avilés; Witold Marciszewski; Grzegorz Plebanek

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

Functional Analysis 2020-04-15 v3

Authors: Antonio Avilés , Witold Marciszewski , Grzegorz Plebanek

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.

Keywords

banach space twisted sum c0 c(k) space weak* topology continuum hypothesis

Cite

@article{arxiv.1902.07783,
  title  = {Twisted sums of $c_0$ and $C(K)$-spaces: A solution to the CCKY problem},
  author = {Antonio Avilés and Witold Marciszewski and Grzegorz Plebanek},
  journal= {arXiv preprint arXiv:1902.07783},
  year   = {2020}
}

Comments

Final version (the previous title `Twisting $c_0$ around nonseparable Banach spaces'), 32 pages

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

Abstract

Keywords

Cite

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