## Simon Fitzpatrick, Bruce Calvert

*Sets invariant under projections onto two dimensional subspaces *

Comment.Math.Univ.Carolinae 32,2 (1991) 233-239. **Abstract:**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 $P(B)\subseteq B$.

**Keywords:** inner product space, two dimensional subspace, projection

**AMS Subject Classification:** 46C05, 52A15

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