On uniform homeomorphisms of the unit spheres of certain Banach lattices
On uniform homeomorphisms of the unit spheres of certain Banach lattices
We prove that if X is an infinite dimensional Banach lattice with a weak unit then there exists a probability space (Ω,Σ,/i) so that the unit sphere of (Li(Ω,Σ,/i)) is uniformly homeomorphic to the unit sphere S(X) if and only if X does not contain Z^'s uniformly.