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arXiv · 1902.10092

On the complete separation of asymptotic structures in Banach spaces

Spiros A. Argyros·Pavlos Motakis
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Abstract

Let $(e_i)_i$ denote the unit vector basis of $\ell_p$, $1\leq p< \infty$, or $c_0$. We construct a reflexive Banach space with an unconditional basis that admits $(e_i)_i$ as a uniformly unique spreading model while it has no subspace with a unique asymptotic model, and hence it has no asymptotic-$\ell_p$ or $c_0$ subspace. This solves a problem of E. Odell. We also construct a space with a unique $\ell_1$ spreading model and no subspace with a uniformly unique $\ell_1$ 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.

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Spiros A. Argyros, Pavlos Motakis. 2019-02-26. On the complete separation of asymptotic structures in Banach spaces. https://arxiv.org/abs/1902.10092

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