A theorem on isotropic spaces
Volume 133 / 1999
Studia Mathematica 133 (1999), 257-260
DOI: 10.4064/sm-133-3-257-260
Abstract
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.
