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Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications
Published online by Cambridge University Press: 20 November 2018
Abstract
We prove that every infinite-dimensional Banach space $X$ having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to
$X\,\backslash \,\left\{ 0 \right\}$. More generally, if
$X$ is an infinite dimensional Banach space and
$F$ is a closed subspace of
$X$ such that there is a real-analytic seminorm on
$X$ whose set of zeros is
$F$, and
$X/F$ is infinite-dimensional, then
$X$ and
$X\backslash F$ are real-analytic diffeomorphic. As an application we show the existence of real-analytic free actions of the circle and the
$n$-torus on certain Banach spaces.
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- Copyright © Canadian Mathematical Society 2002