A weak Asplund space whose dual is not weak* fragmentable

Kenderov, Petar; Moors, Warren; Sciffer, Scott

doi:10.1090/S0002-9939-01-06002-6

A weak Asplund space whose dual is not weak$^*$ fragmentable
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by Petar S. Kenderov, Warren B. Moors and Scott Sciffer PDF

Proc. Amer. Math. Soc. 129 (2001), 3741-3747 Request permission

Abstract:

Under the assumption that there exists in the unit interval $[0,1]$ an uncountable set $A$ with the property that every continuous mapping from a Baire metric space $B$ into $A$ is constant on some non-empty open subset of $B$, we construct a Banach space $X$ such that $(X^*, \mathrm {weak}^*)$ belongs to Stegall’s class but $(X^*, \mathrm {weak}^*)$ is not fragmentable.

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