arXiv:math/9207208 Abstract

arXiv:math/9207208 [math.FA]Abstract References Reviews Resources

On Uniform Homeomorphisms of the Unit Spheres of Certain Banach Lattices

Published 1992-07-21Version 1

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.

Categories: math.FA

Keywords: unit sphere, uniform homeomorphisms, infinite dimensional banach lattice, weak unit, probability space

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