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A note on the Banach-Mazur problem

Published online by Cambridge University Press:  01 January 2002

Beata Randrianantoanina
Beata Randrianantoanina
Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, USA e-mail: randrib@muohio.edu
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We prove that if X is a real Banach space, with dim X\ge 3, which contains 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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 1 , January 2002 , pp. 159 - 165
Copyright
2002 Glasgow Mathematical Journal Trust