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In mathematics, the Milman–Pettis theorem states that every uniformly convex Banach space is reflexive. The theorem was proved independently by D. Milman (1938) and B. J. Pettis (1939). S. Kakutani gave a different proof in 1939, and John R. Ringrose published a shorter proof in 1959. Mahlon M. Day (1941) gave examples of reflexive Banach spaces which are not isomorphic to any uniformly convex space. == References == * S. Kakutani, ''Weak topologies and regularity of Banach spaces'', Proc. Imp. Acad. Tokyo 15 (1939), 169–173. * D. Milman, ''On some criteria for the regularity of spaces of type (B)'', C. R. (Doklady) Acad. Sci. U.R.S.S, 20 (1938), 243–246. * B. J. Pettis, ''A proof that every uniformly convex space is reflexive'', Duke Math. J. 5 (1939), 249–253. * J. R. Ringrose, ''A note on uniformly convex spaces'', J. London Math. Soc. 34 (1959), 92. * fr:Théorème de Milman-Pettis 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「Milman–Pettis theorem」の詳細全文を読む スポンサード リンク
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