On the complete separation of unique ${\ell }_1$ spreading models and the Lebesgue property of Banach spaces

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.

23 pages

References in corpus (1)

• Separable Spaces of Continuous Functions as Calkin Algebras