Titlebook: Best Approximation in Inner Product Spaces; Frank Deutsch Textbook 2001 Springer-Verlag New York 2001 Convexity.Hilbert space.algorithms.c

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Bounded Linear Functionals and Best Approximation from Hyperplanes and Half-Spaces,sely those that “attain their norm” (Theorem 6.12). We should mention that many of the results of this chapter—particularly those up to Theorem 6.12—can be substantially simplified or omitted entirely if the space . is assumed ., i.e., if . is a Hilbert space. Because many of the important spaces th

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Best Approximation in Inner Product Spaces978-1-4684-9298-9Series ISSN 1613-5237 Series E-ISSN 2197-4152

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Existence and Uniqueness of Best Approximations,ce theorems of interest. In particular, the two most useful existence and uniqueness theorems can be deduced from it. They are: (1) Every finite-dimensional subspace is Chebyshev, and (2) every closed convex subset of a Hilbert space is Chebyshev.

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