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On the complete separation of asymptotic structures in Banach spaces
Advances in Mathematics ( IF 1.435 ) Pub Date : 2020-01-08 , DOI: 10.1016/j.aim.2019.106962
Spiros A. Argyros; Pavlos Motakis

Let (ei)i denote the unit vector basis of ℓp, 1≤p<∞, or c0. We construct a reflexive Banach space with an unconditional basis that admits (ei)i as a uniformly unique spreading model while it has no subspace with a unique asymptotic model, and hence it has no asymptotic-ℓp or c0 subspace. This solves a problem of E. Odell. We also construct a space with a unique ℓ1 spreading model and no subspace with a uniformly unique ℓ1 spreading model. These results are achieved with the utilization of a new version of the method of saturation under constraints that uses sequences of functionals with increasing weights.
更新日期:2020-01-08

 

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