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Winning tactics in a geometrical game
Author(s):
Antonín
Procházka
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1051-1061.
MSC (2000):
Primary 91A05, 46B20, 46B22;
Secondary 47H04
Posted:
September 26, 2008
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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.
References:
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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:
10.1090/S0002-9939-08-09636-6
PII:
S 0002-9939(08)09636-6
Keywords:
Point-slice game,
Radon-Nikod\'ym property characterization,
superreflexivity characterization
Received by editor(s):
February 18, 2008
Posted:
September 26, 2008
Additional Notes:
The author was supported by the grant GA CR 201/07/0394.
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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