Two games, two dichotomies: stability and independence in Banach spaces
Preprints · José Iovino
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We show that two games on the space of types of a separable Banach space decide stability and independence: Player II wins the commitment game for every type exactly when the space is stable, and wins the revision game for every type exactly when the space has no independent sequence. In each game the alternative is a winning strategy for Player I, read off from an infinite ladder or from an independent sequence; each game therefore yields a dichotomy with a margin. Among block subspaces, the dichotomy for stability holds up to a parameter, and the uniformly wild alternative excludes every subspace close to a stable space.
- Two games, two dichotomies: stability and independence in Banach spaces PDF