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

2019/02/20 by Avilés, Antonio, Marciszewski, Witold, Plebanek, Grzegorz
#03E35 #46B25 #46B26 #46E15 (Primary) #54C55 #54D40 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1902.07783

Abstract

We consider the class of Banach space Y for which c₀ admits a nontrivial twisted sum with Y. We present a characterization of such space 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 positive solution to a problem posed by Cabello, Castillo, Kalton and Yost.

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