Charles University in Prague, Faculty of Mathematics and Physics
Abstract
summary:The Blaschke--Kakutani result characterizes inner product spaces E, among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace F there is a norm 1 linear projection onto F. In this paper, we determine which closed neighborhoods B of zero in a real locally convex space E of dimension at least 3 have the property that for every 2 dimensional subspace F there is a continuous linear projection P onto F with P(B)⊆B