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James' theorem : ウィキペディア英語版
James' theorem
In mathematics, particularly functional analysis, James' theorem, named for Robert C. James, states that a Banach space ''B'' is reflexive if and only if every continuous linear functional on ''B'' attains its maximum on the closed unit ball in ''B''.
A stronger version of the theorem states that a weakly closed subset ''C'' of a Banach space ''B'' is weakly compact if and only if each continuous linear functional on ''B'' attains a maximum on ''C''.
The hypothesis of completeness in the theorem cannot be dropped .
== See also ==

*Banach–Alaoglu theorem
*Bishop–Phelps theorem
*Eberlein–Šmulian theorem
*Mazur's lemma
*Goldstine theorem

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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