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Linearization of certain uniform homeomorphisms

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

Anthony Weston
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: X →Y, 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.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces 46B04: Isometric theory of Banach spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 1 , February 2007 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 2007

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