Characterizations of Inner Product Spaces |
Contents
Structure | 1 |
Area calculation arguments and area orthogonalities | 8 |
Kakutanis conditions | 101 |
Copyright | |
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½½ 2-dimensional space 2-dimensional subspace Amer Banach spaces best approximation bounded characterizations of inner chord closed maximal subspace condition conv convA convex set dimensional ellipsoid embeds in E2 equivalent Euclidean Figure geometric Hahn-Banach theorem hence Hilbert spaces hyperplane implies strict convexity inequality inner product spaces intersection isoceles triangle isometry Jour Lemma linear projection linear selection M₂ Math metric projection nonexpansive norm-1 projection normed linear spaces normed space P.L. Papini parallelogram parallelogram equality plane points Proc Proof of i.p.s properties proximinal S₁ satisfies segment sgnx sgny smooth strictly convex subspace F supporting hyperplane tangent theorem triangle twice differentiable ty ² unique unit sphere Vu,v