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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)』 ■ウィキペディアで「James' theorem」の詳細全文を読む
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