On Uniform Homeomorphisms of the Unit Spheres of Certain Banach Lattices

Details On Uniform Homeomorphisms of the Unit Spheres of Certain Banach Lattices On Uniform Homeomorphisms of the Unit Spheres of Certain Banach Lattices

1992-07-21

arxiv.org/abs/math/9207208v1

Mathematics

Functional Analysis

Scientific paper

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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