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Results tagged with hilbert-spaces
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user 32507
A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.
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Are the intersection of proximinal sets in a Hilbert Space proximinal?
This answer is strongly inspired by example 3.11 in the book by Bauschke and Combettes.
Let $H = \ell^2$ and consider a sequence $\{\alpha_n\} \in (1,\infty)$ with $\alpha_n \searrow 1$. Define
\begi …
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