This is an announcement for the paper "Convex-transitive characterizations of Hilbert spaces" by Jarno Talponen.
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.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46C15
The source file(s), amsct2.tex: 89202 bytes, is(are) stored in gzipped form as 0705.2526.gz with size 24kb. The corresponding postcript file has gzipped size 142kb.
Submitted from: talponen@cc.helsinki.fi
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