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

Frerking, J.; Westphal, U.

doi:10.1090/S0002-9939-1989-0946636-6

On a property of metric projections onto closed subsets of Hilbert spaces
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by J. Frerking and U. Westphal PDF

Proc. Amer. Math. Soc. 105 (1989), 644-651 Request permission

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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