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arXiv · 2402.14687

On the complete separation of unique $\ell_{1}$ spreading models and the Lebesgue property of Banach spaces

Harrison Gaebler·Pavlos Motakis·Bunyamin Sari
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Abstract

We construct a reflexive Banach space $X_\mathcal{D}$ with an unconditional basis such that all spreading models admitted by normalized block sequences in $X_\mathcal{D}$ are uniformly equivalent to the unit vector basis of $\ell_1$, yet every infinite-dimensional closed subspace of $X_\mathcal{D}$ fails the Lebesgue property. This is a new result in a program initiated by Odell in 2002 concerning the strong separation of asymptotic properties in Banach spaces.

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Harrison Gaebler, Pavlos Motakis, Bunyamin Sari. 2024-02-22. On the complete separation of unique $\ell_{1}$ spreading models and the Lebesgue property of Banach spaces. https://doi.org/10.4153/s0008414x24000786

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