Winning tactics in a geometrical game

Procházka, Antonín

doi:10.1090/S0002-9939-08-09636-6

Winning tactics in a geometrical game
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by Antonín Procházka PDF

Proc. Amer. Math. Soc. 137 (2009), 1051-1061 Request permission

Abstract:

A winning tactic for the point-closed slice game in a closed bounded convex set $K$ with Radon-Nikodým property (RNP) is constructed. Consequently a Banach space $X$ has the RNP if and only if there exists a winning tactic in the point-closed slice game played in the unit ball of $X$. By contrast, there is no winning tactic in the point-open slice game in $K$. Finally, a more subtle analysis of the properties of the winning tactics leads to a characterization of superreflexive spaces.

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