J. Aust. Math. Soc.  82 (2007), 1-9
Linearization of certain uniform homeomorphisms

Anthony Weston
  Department of Mathematics and Statistics
  Canisius College
  Buffalo, NY 14208
  USA
  westona@canisius.edu


Abstract
This article concerns the uniform classification of infinite dimensional real topological vector spaces. We examine a recently isolated linearization procedure for uniform homeomorphisms of the form $\phi : X \to Y$, where $X$ is a Banach space with non-trivial type and $Y$ is any topological vector space. For such a uniform homeomorphism $\phi$, we show that $Y$ must be normable and have the same supremal type as $X$. That $Y$ is normable generalizes theorems of Bessaga and Enflo. This aspect of the theory determines new examples of uniform non-equivalence. That supremal type is a uniform invariant for Banach spaces is essentially due to Ribe. Our linearization approach gives an interesting new proof of Ribe's result.
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