Best approximation in $L^ 1(I,X)$
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- by R. Khalil and F. Saidi PDF
- Proc. Amer. Math. Soc. 123 (1995), 183-190 Request permission
Abstract:
Let X be a Banach space and G a closed subspace of X. The subspace G is called proximinal in X if for every $x \in X$ there exists at least one $y \in G$ such that $\left \| {x - y} \right \| = d(x,G) = \inf \{ \left \| {x - z} \right \|:z \in G\}$. It is an open problem whether ${L^1}(I,G)$ is proximinal in ${L^1}(I,X)$ if G is proximinal in X, where I is the unit interval with the Lebesgue measure. In this paper, we prove the proximinality of ${L^1}(I,G)$ in ${L^1}(I,X)$ for a class of proximinal subspaces G in X.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 183-190
- MSC: Primary 41A65; Secondary 46E40
- DOI: https://doi.org/10.1090/S0002-9939-1995-1223266-5
- MathSciNet review: 1223266