Advances in Mathematics ( IF 1.494 ) Pub Date : 2020-01-08 , DOI: 10.1016/j.aim.2019.106962 Spiros A. Argyros; Pavlos Motakis
Let denote the unit vector basis of , , or . We construct a reflexive Banach space with an unconditional basis that admits as a uniformly unique spreading model while it has no subspace with a unique asymptotic model, and hence it has no asymptotic- or subspace. This solves a problem of E. Odell. We also construct a space with a unique spreading model and no subspace with a uniformly unique 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.