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2 Existence of elements of best approximation
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Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces
Limited preview - 2013
A. L. Garkavi 66 arbitrary assume Banach space best approximation Borel sets Cebysev subspace Cebysev system Chap closed linear subspaces compact space completes the proof conjugate space Consequently convex set corollary 1.9 CR(Q defined E. E. Phelps Eadon measure element xeE elements of best extremal points finite codimension G a linear G is proximinal given h numbers hence implication inner product space isometry Krein-Milman theorem Lebesgue measure lemma let G linear manifold linearly independent maximal element metric space n-dimensional linear subspace non-void normed linear space obtain particular polynomial positive measure space proof of lemma proof of theorem Q compact satisfies 1.2 scalars are complex scalars are real semi-Cebysev subspace sequence space Q SPACES C(Q statements are equivalent strictly convex subspace G subspace of finite taking into account theorem 1.1 unit cell virtue of theorem weak topology whence