Proximinality of certain subspaces of \(C_ b(S;E)\) (Q913178)
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scientific article; zbMATH DE number 4146785
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Proximinality of certain subspaces of \(C_ b(S;E)\) |
scientific article; zbMATH DE number 4146785 |
Statements
Proximinality of certain subspaces of \(C_ b(S;E)\) (English)
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1989
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Let S be a completely regular Hausdorff space and let E be a Banach space. Let \(C_ b(S;E)\) be the Banach space of all continuous and bounded functions from S into E, equipped with the supremum-norm \(\| f\| =\sup \{\| f(x)\|;\quad x\in S\}.\) Given a proximinal linear subspace V of E, we study conditions under which the space \(\{f\in C_ b(S;E)\); f(S)\(\subset V\}\) is also proximinal in \(C_ b(S;E)\).
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proximinal subspace
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proximity maps
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