On isometric reflexions in Banach spaces
Functional Analysis
2016-09-06 v1
Abstract
We obtain the following characterization of Hilbert spaces. Let be a Banach space whose unit sphere has a hyperplane of symmetry. Then is a Hilbert space iff any of the following two conditions is fulfilled: a) the isometry group of has a dense orbit in S; b) the identity component of the group endowed with the strong operator topology acts topologically irreducible on . Some related results on infinite dimentional Coxeter groups generated by isometric reflexions are given which allow to analyse the structure of isometry groups containing sufficiently many reflexions.
Cite
@article{arxiv.math/9512204,
title = {On isometric reflexions in Banach spaces},
author = {A. Skorik and Mikhail Zaidenberg},
journal= {arXiv preprint arXiv:math/9512204},
year = {2016}
}