Geodesic
Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications
Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 3-10

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DOI

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.
DOI : 10.4153/CMB-2002-001-7
Mots-clés : 46B20, 58B99 
Azagra, D.; Dobrowolski, T. Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications. Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 3-10. doi: 10.4153/CMB-2002-001-7
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     title = {Real-Analytic {Negligibility} of {Points} and {Subspaces} in {Banach} {Spaces,} with {Applications}},
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     year = {2002},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-001-7/}
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