A weak* separable 𝐶(𝐾)* space whose unit ball is not weak* separable

Avilés, A.; Plebanek, G.; Rodríguez, J.

doi:10.1090/S0002-9947-2014-05962-X

A weak$^$ separable $C(K)^$ space whose unit ball is not weak$^*$ separable
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by A. Avilés, G. Plebanek and J. Rodríguez PDF

Trans. Amer. Math. Soc. 366 (2014), 4733-4753 Request permission

Abstract:

We provide a ZFC example of a compact space $K$ such that $C(K)^*$ is $w^*$-separable but its closed unit ball $B_{C(K)^*}$ is not $w^*$-separable. All previous examples of such kind had been constructed under CH. We also discuss the measurability of the supremum norm on that $C(K)$ equipped with its weak Baire $\sigma$-algebra.

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