J. Aust. Math. Soc.
82 (2007), 19

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
, where
is a Banach space with nontrivial type and
is any topological vector space. For such a
uniform homeomorphism
, we show that
must be normable and have the same supremal type
as
. That
is normable generalizes theorems of Bessaga and
Enflo. This aspect of the theory determines new
examples of uniform nonequivalence. 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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