On subclasses of weak Asplund spaces

Kalenda, Ondřej; Kunen, Kenneth

doi:10.1090/S0002-9939-04-07744-5

On subclasses of weak Asplund spaces
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by Ondřej F. K. Kalenda and Kenneth Kunen PDF

Proc. Amer. Math. Soc. 133 (2005), 425-429 Request permission

Abstract:

Assuming the consistency of the existence of a measurable cardinal, it is consistent to have two Banach spaces, $X,Y$, where $X$ is a weak Asplund space such that $X^{*}$ (in the weak* topology) in not in Stegall’s class, whereas $Y^{*}$ is in Stegall’s class but is not weak* fragmentable.

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