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On the complete separation of unique $\ell_{1}$ spreading models and the Lebesgue property of Banach spaces
- Publication Year :
- 2024
-
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.<br />Comment: 23 pages
- Subjects :
- Mathematics - Functional Analysis
46B06, 46B20, 46B25, 46G12
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.14687
- Document Type :
- Working Paper