2007/05/17 by Jarno Talponen, Talponen, Jarno
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.0705.2526
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.