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On Uniform Homeomorphisms of the Unit Spheres of Certain Banach Lattices

Fouad Chaatit
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Abstract

We prove that if X is an infinite dimensional Banach lattice with a weak unit then there exists a probability space (Omega, Sigma,mu) so that the unit sphere S(L_1(Omega, Sigma, mu) is uniformly homeomorphic to the unit sphere S(X) if and only if X does not contain l_{infty}^n's uniformly.

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Fouad Chaatit. 1992-07-21. On Uniform Homeomorphisms of the Unit Spheres of Certain Banach Lattices. https://arxiv.org/abs/math/9207208

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