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

DOI:
https://doi.org/10.1090/S0002-9939-08-09636-6

Published electronically:
September 26, 2008

MathSciNet review:
2457446

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A winning tactic for the point-closed slice game in a closed bounded convex set with Radon-Nikodým property (RNP) is constructed. Consequently a Banach space has the RNP if and only if there exists a winning tactic in the point-closed slice game played in the unit ball of . By contrast, there is no winning tactic in the point-open slice game in . 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

Email:
protony@math.u-bordeaux1.fr

DOI:
https://doi.org/10.1090/S0002-9939-08-09636-6

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.