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A note on Banach--Mazur problem

Beata Randrianantoanina
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Abstract

We prove that if $X$ is a real Banach space, with $\dim X\geq 3$, which contains a subspace of codimension 1 which is 1-complemented in $X$ and whose group of isometries is almost transitive then $X$ is isometric to a Hilbert space. This partially answers the Banach-Mazur rotation problem and generalizes some recent related results.

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Beata Randrianantoanina. 2001-10-18. A note on Banach--Mazur problem. https://arxiv.org/abs/math/0110202

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