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- W2154111999 abstract "A Banach space X is said to have property ( PROXBID ) if the canonical image of X in its bidual X ** is proximal. In other words, if J : X → X ** is the canonical embedding, then it is required that every element of X ** have at least one best approximation (i.e., nearest point) from the closed subspace J ( X ). We show below that, if X is the space of (real or complex) continuous functions on a compact set, or the space of (real or complex) continuous functions that vanish at infinity on a locally compact set, then X has property (PROXBID). At this point we should mention the existence of a variety of examples [2, 8] of Banach spaces which lack property (PROXBID)." @default.
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- W2154111999 date "1974-03-01" @default.
- W2154111999 modified "2023-09-25" @default.
- W2154111999 title "An approximative property of spaces of continuous functions" @default.
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- W2154111999 doi "https://doi.org/10.1017/s001708950000210x" @default.
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