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arXiv · 1112.5710

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

Antonio Avilés·Grzegorz Plebanek·José Rodríguez
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Abstract

We provide a ZFC example of a compact space K such that C(K)* is w*-separable but its closed unit ball 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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Antonio Avilés, Grzegorz Plebanek, José Rodríguez. 2011-12-24. A weak* separable C(K)* space whose unit ball is not weak* separable. https://arxiv.org/abs/1112.5710

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