Milman–Pettis theorem

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.

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.