Geodesic
Special symmetries of Banach spaces isomorphic to Hilbert spaces
Jarno Talponen1
1 Institute of Mathematics Aalto University P.O. Box 1100 FI-00076 Aalto, Finland
Studia Mathematica, Tome 200 (2010) no. 1, pp. 31-40

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We characterize Hilbert spaces among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.
DOI : 10.4064/sm200-1-2
Keywords: characterize hilbert spaces among banach spaces terms transitivity respect nicely behaved subgroups isometry group example following result typical real banach space isomorphic hilbert space convex transitive respect isometric finite dimensional perturbations identity already isometric hilbert space

Jarno Talponen 1

1 Institute of Mathematics Aalto University P.O. Box 1100 FI-00076 Aalto, Finland 
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Jarno Talponen. Special symmetries of Banach spaces isomorphic to Hilbert spaces. Studia Mathematica, Tome 200 (2010) no. 1, pp. 31-40. doi: 10.4064/sm200-1-2

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