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

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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