A new infinite game in Banach spaces with applications

dc.creatorOdell, Edward
dc.creatorSchlumprecht, Thomas
dc.creatorZsák, András
dc.date2007-06-05
dc.date.accessioned2026-07-07T08:04:12Z
dc.date.available2026-07-07T08:04:12Z
dc.descriptionWe consider the following two-player game played on a separable, infinite-dimensional Banach space X. Player S chooses a positive integer k_1 and a finite-codimensional subspace X_1 of X. Then player P chooses x_1 in the unit sphere of X_1. Moves alternate thusly, forever. We study this game in the following setting. Certain normalized, 1-unconditional sequences (u_i) and (v_i) are fixed so that S has a winning strategy to force P to select x_i's so that if the moves are (k_1,X_1,x_1,k_2,X_2,x_2,...), then (x_i) is dominated by (u_{k_i}) and/or (x_i) dominates (v_{k_i}). In particular, we show that for suitable (u_i) and (v_i) if X is reflexive and S can win both of the games above, then X embeds into a reflexive space Z with an FDD which also satisfies analogous block upper (u_i) and lower (v_i) estimates. Certain universal space consequences ensue.
dc.description30 pages, uses mypreamble.tex
dc.identifierhttps://arxiv.org/abs/0706.0651
dc.identifierhttp://arxiv.org/abs/0706.0651
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129863
dc.subjectFunctional Analysis
dc.subject46B20
dc.titleA new infinite game in Banach spaces with applications
dc.typetext

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