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

Azagra, D. ; Dobrowolski, T.

Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 3-10

Résumé

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.

Détail

DOI : 10.4153/CMB-2002-001-7

Mots-clés : 46B20, 58B99

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