%0 Journal Article
%T Convex-transitive characterizations of Hilbert spaces
%A Jarno Talponen
%J Mathematics
%D 2007
%I arXiv
%X In this paper we investigate real convex-transitive Banach spaces X, which admit a 1-dimensional bicontractive projection P on X. Various mild conditions regarding the weak topology and the geometry of the norm are provided, which guarantee that such an X is in fact isometrically a Hilbert space. The results obtained can be regarded as partial answers to the well-known Banach-Mazur rotation problem, as well as to a question posed by B. Randrianantoanina in 2002 about convex-transitive spaces.
%U http://arxiv.org/abs/0705.2526v2