Infinite asymptotic games

Christian Rosendal[1]

  • [1] University of Illinois at Chicago Department of Mathematics, Statistics and Computer Science 322 Science and Engineering Offices (M/C 249) 851 S. Morgan Street Chicago, IL 60607-7045 (USA)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 4, page 1359-1384
  • ISSN: 0373-0956

Abstract

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We study infinite asymptotic games in Banach spaces with a finite-dimensional decomposition (F.D.D.) and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into ℓ p sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. The results are related to questions of rapidity of subsequence extraction from normalised weakly null sequences.

How to cite

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Rosendal, Christian. "Infinite asymptotic games." Annales de l’institut Fourier 59.4 (2009): 1359-1384. <http://eudml.org/doc/10431>.

@article{Rosendal2009,
abstract = {We study infinite asymptotic games in Banach spaces with a finite-dimensional decomposition (F.D.D.) and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into $\ell _p$ sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. The results are related to questions of rapidity of subsequence extraction from normalised weakly null sequences.},
affiliation = {University of Illinois at Chicago Department of Mathematics, Statistics and Computer Science 322 Science and Engineering Offices (M/C 249) 851 S. Morgan Street Chicago, IL 60607-7045 (USA)},
author = {Rosendal, Christian},
journal = {Annales de l’institut Fourier},
keywords = {Infinite asymptotic games; extraction of subsequences; weakly null trees; infinite asymptotic games; subsequence game; block trees},
language = {eng},
number = {4},
pages = {1359-1384},
publisher = {Association des Annales de l’institut Fourier},
title = {Infinite asymptotic games},
url = {http://eudml.org/doc/10431},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Rosendal, Christian
TI - Infinite asymptotic games
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 4
SP - 1359
EP - 1384
AB - We study infinite asymptotic games in Banach spaces with a finite-dimensional decomposition (F.D.D.) and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into $\ell _p$ sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. The results are related to questions of rapidity of subsequence extraction from normalised weakly null sequences.
LA - eng
KW - Infinite asymptotic games; extraction of subsequences; weakly null trees; infinite asymptotic games; subsequence game; block trees
UR - http://eudml.org/doc/10431
ER -

References

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  13. B. Maurey, V. D. Milman, N. Tomczak-Jaegermann, Asymptotic infinite-dimensional theory of Banach spaces, Geometric aspects of functional analysis (Israel, 1992–1994) 77 (1995), 149-175, Birkhäuser, Basel Zbl0872.46013MR1353458
  14. E. Odell, Th. Schlumprecht, Trees and branches in Banach spaces, Trans. Amer. Math. Soc. 354 (2002), 4085-4108 Zbl1023.46014MR1926866
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  17. C. Rosendal, An exact Ramsey principle for block sequences Zbl1198.46006

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