A new infinite game in Banach spaces with applications
| dc.creator | Odell, Edward | |
| dc.creator | Schlumprecht, Thomas | |
| dc.creator | Zsák, András | |
| dc.date | 2007-06-05 | |
| dc.date.accessioned | 2026-07-07T08:04:12Z | |
| dc.date.available | 2026-07-07T08:04:12Z | |
| dc.description | We 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.description | 30 pages, uses mypreamble.tex | |
| dc.identifier | https://arxiv.org/abs/0706.0651 | |
| dc.identifier | http://arxiv.org/abs/0706.0651 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129863 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20 | |
| dc.title | A new infinite game in Banach spaces with applications | |
| dc.type | text |