A theorem on isotropic spaces

Volume 133 / 1999

Félix Cabello Sánchez Studia Mathematica 133 (1999), 257-260 DOI: 10.4064/sm-133-3-257-260


Let X be a normed space and $G_F(X)$ the group of all linear surjective isometries of X that are finite-dimensional perturbations of the identity. We prove that if $G_F(X)$ acts transitively on the unit sphere then X must be an inner product space.


  • Félix Cabello Sánchez

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