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Linearization of certain uniform homeomorphisms

Published online by Cambridge University Press:  09 April 2009

Anthony Weston
Affiliation:
Department of Mathematics & StatisticsCanisius CollegeBuffalo, NY 14208USA e-mail: [email protected]
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Abstract

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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 φ: XY, where X is a Banach space with non-trivial type and Y is any topological vector space. For such a uniform homeomorphism φ, 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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

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