Twisted sums of c0 and C(K)-spaces: A solution to the CCKY problem

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 propertiesof the weak^∗ topology on Y^∗. We prove that under the continuum hypothesis c₀ has anontrivial twisted sum with every space of the form Y=C(K), where K is compact andnot metrizable. This gives a consistent affirmative solution to a problem posed by Cabello,Castillo, Kalton and Yost.