m at h . FA ] 6 D ec 1 99 5 On isometric reflexions in Banach spaces ∗
نویسنده
چکیده
We obtain the following characterization of Hilbert spaces. Let E be a Banach space whose unit sphere S has a hyperplane of symmetry. Then E is a Hilbert space iff any of the following two conditions is fulfilled: a) the isometry group Iso E of E has a dense orbit in S; b) the identity component G 0 of the group Iso E endowed with the strong operator topology acts topologically irreducible on E. 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.
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