Abstract
We consider the class of Banach spaces Y for which c0 admits a nontrivial twisted sum with Y. We present a characterization of such spaces Y in terms of properties of the weak⁎ topology on Y⁎. We prove that under the continuum hypothesis c0 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 affirmative solution to a problem posed by Cabello, Castillo, Kalton and Yost.
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