Convex-transitive characterizations of Hilbert spaces
Functional Analysis
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.0705.2526,
title = {Convex-transitive characterizations of Hilbert spaces},
author = {Jarno Talponen},
journal= {arXiv preprint arXiv:0705.2526},
year = {2007}
}