# 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

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topRosendal, 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 -

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