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Orlicz–Pettis theorem : ウィキペディア英語版 | Orlicz–Pettis theorem In functional analysis, the Orlicz–Pettis theorem is a theorem about convergence in Banach spaces. It is named for Władysław Orlicz and Billy James Pettis.〔.〕〔.〕 The result was originally proven by Orlicz for weakly sequentially complete normed spaces.〔.〕 == Orlicz–Pettis Theorem for Banach spaces == Let ''X'' be a Banach space and let be any sequence in ''X''. If the series is weakly subseries convergent, then the series is actually subseries convergent in the norm topology of ''X''.
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「Orlicz–Pettis theorem」の詳細全文を読む
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