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Bishop–Phelps theorem

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Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionDec 27, 2023
Entity authorityQ16842437 ↗
Source-derived summary

In mathematics, the Bishop–Phelps theorem is a theorem about the topological properties of Banach spaces named after Errett Bishop and Robert Phelps, who published its proof in 1961.

Statement

Importantly, this theorem fails for complex Banach spaces.

However, for the special case where

B

{\displaystyle B}

is the closed unit ball then this theorem does hold for complex Banach spaces.

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The public source identifies “Bishop–Phelps theorem” as open-knowledge reference entry. This brief keeps that definition visible, then builds a research path around Bishop, Phelps and theorem.

Editorial reviewA practical starting point whose main value is the path it opens into stronger specialist and primary sources. The current lead gives the account dated anchors—1961—that can be checked directly. The selected authority fields contribute no independent date. Its value is orientation rather than verdict, with Bishop, Phelps and theorem providing the first useful test.
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The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated Dec 27, 2023. The linked authority identifier is Q16842437. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1961.

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Source & attribution

This entry incorporates text from “Bishop–Phelps theorem” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.