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On the complete separation of unique
$\ell _{1}$ spreading models and the Lebesgue property of Banach spaces
- Part of
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- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 13 December 2024, pp. 1-23
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- Article
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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.
