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Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications

  Published:2002-03-01
 Printed: Mar 2002
  • D. Azagra
  • T. Dobrowolski
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Abstract

We prove that every infinite-dimensional Banach space $X$ having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to $X \setminus \{0\}$. 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 $X \setminus F$ 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.
MSC Classifications: 46B20, 58B99 show english descriptions Geometry and structure of normed linear spaces
None of the above, but in this section
46B20 - Geometry and structure of normed linear spaces
58B99 - None of the above, but in this section
 

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