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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a property of metric projections onto closed subsets of Hilbert spaces


Authors: J. Frerking and U. Westphal
Journal: Proc. Amer. Math. Soc. 105 (1989), 644-651
MSC: Primary 41A65; Secondary 41A52, 46C05, 47H05
DOI: https://doi.org/10.1090/S0002-9939-1989-0946636-6
MathSciNet review: 946636
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Abstract: Applying the theory of monotone operators to the metric projection $ {P_K}$ of a Hilbert space $ H$ onto a nonempty closed subset $ K$ of $ H$ we prove a kind of connectedness property of the set $ \{ x \in H;{P_K}(x)$ is not a singleton or $ {P_K}$ is not upper semi-continuous at $ x\} $ which is a typical set for investigations in best approximation. A result of Balaganskii is extended.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0946636-6
Keywords: Best approximation in Hilbert spaces, convexity of Chebyshev sets, continuity of metric projections, uniqueness in best approximation, monotony of metric projections
Article copyright: © Copyright 1989 American Mathematical Society