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Winning tactics in a geometrical game

Author: Antonín Procházka
Journal: Proc. Amer. Math. Soc. 137 (2009), 1051-1061
MSC (2000): Primary 91A05, 46B20, 46B22; Secondary 47H04
Published electronically: September 26, 2008
MathSciNet review: 2457446
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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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Additional Information

Antonín Procházka
Affiliation: KMA MFF UK, Charles University, Sokolovská 83, 18675 Prague, Czech Republic
Address at time of publication: Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex, France

Keywords: Point-slice game, Radon-Nikod\'ym property characterization, superreflexivity characterization
Received by editor(s): February 18, 2008
Published electronically: September 26, 2008
Additional Notes: The author was supported by the grant GA CR 201/07/0394.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.