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


Its statement is as follows.
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: Let ''B''&nbsp;⊂&nbsp;''E'' be a bounded, closed, convex set of a Banach space&nbsp;''E''. Then the set
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:: <math>\{e^*\in E^*\mid e^* \text{ attains its supremum on } B\}</math>
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: is norm-dense in the dual <math>E^*</math>.
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==See also==
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*[[Banach–Alaoglu theorem]]
 
*[[Eberlein–Šmulian theorem]]
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*[[Mazur's lemma]]
 
*[[James' theorem]]
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*[[Goldstine theorem]]
 
 
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==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}}
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{{DEFAULTSORT:Bishop-Phelps theorem}}
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[[Category:Theorems in functional analysis]]
 
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Revision as of 06:00, 10 February 2014

heavy mental burden

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