A weak* separable C(K)* space whose unit ball is not weak* separable
Functional Analysis
2014-06-30 v1 General Topology
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.
Keywords
Cite
@article{arxiv.1112.5710,
title = {A weak* separable C(K)* space whose unit ball is not weak* separable},
author = {Antonio Avilés and Grzegorz Plebanek and José Rodríguez},
journal= {arXiv preprint arXiv:1112.5710},
year = {2014}
}