Convex-transitive characterizations of Hilbert spaces

Jarno Talponen

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arXiv · 0705.2526

Convex-transitive characterizations of Hilbert spaces

Jarno Talponen

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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.

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BibTeX RIS

Jarno Talponen. 2007-05-18. Convex-transitive characterizations of Hilbert spaces. https://arxiv.org/abs/0705.2526

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