This is an announcement for the paper "Infinite asymptotic games" by Christian Rosendal.
Abstract: We study infinite asymptotic games in Banach spaces with an 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. These results are related to questions of rapidity of subsequence extraction from normalised weakly null sequences.
Archive classification: math.FA math.LO
Mathematics Subject Classification: Primary: 46B03, Secondary 03E15
The source file(s), AsymptoticGames42.tex: 71838 bytes, is(are) stored in gzipped form as 0608616.gz with size 22kb. The corresponding postcript file has gzipped size 0kb.
Submitted from: rosendal@math.uiuc.edu
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