Pacific Journal of Mathematics

On uniform homeomorphisms of the unit spheres of certain Banach lattices.

Fouad Chaatit

Article information

Pacific J. Math., Volume 168, Number 1 (1995), 11-31.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B42: Banach lattices [See also 46A40, 46B40]


Chaatit, Fouad. On uniform homeomorphisms of the unit spheres of certain Banach lattices. Pacific J. Math. 168 (1995), no. 1, 11--31.

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  • [2] The main result. We now state the main result of this work. THEOREM 2.1.Let X be an infinite dimensional Banach lattice with a weak unit. Then there exists a probability space (, , ) so that 5(L(, , )) is uniformly homeomorphic to S(X) if and only if X does not contain /^ uniformly in n. Our proof of Theorem 2.1 will yield two quantitative results:
  • [L T] Then the proof goes as in [O.S]. By a theorem of Maurey and Pisier [MP] X must have a finite cotype q'. Thus X is g-concave, in fact for all q > q' ([L.T, p.88]). Renorm X by an equivalent norm for which Mq(X) = 1 and such that X has the same lattice
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