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In mathematics, the '''Bishop–Phelps theorem''' is due to [[Errett Bishop]] and [[Robert Phelps]].

Its statement is as follows.

: Let ''B''&nbsp;⊂&nbsp;''E'' be a bounded, closed, convex set of a Banach space&nbsp;''E''. Then the set

:: <math>\{e^*\in E^*\mid e^* \text{ attains its supremum on } B\}</math>

: is norm-dense in the dual <math>E^*</math>.

==See also==
*[[Banach–Alaoglu theorem]]
*[[Eberlein–Šmulian theorem]]
*[[Mazur's lemma]]
*[[James' theorem]]
*[[Goldstine theorem]]

==References==
* {{cite journal|last1=Bishop|first1=Errett|authorlink1=Errett Bishop|last2=Phelps|first2=R. R.|authorlink2=Robert R. Phelps|title=A proof that every Banach space is subreflexive|journal=Bulletin of the American Mathematical Society|volume=67|year=1961|pages=97–98|mr=123174|ref=harv}}

{{DEFAULTSORT:Bishop-Phelps theorem}}
[[Category:Theorems in functional analysis]]
{{Functional Analysis}}

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