On the Banach-Saks property (Q1080110)

The main result is stated as follows: Let X be a Banach space with a uniformly convex conjugate space \(X^*\). Then X possesses the Banach-Saks property. After we have proved the above theorem, we find the following result due to \textit{P. Enflo} [J. Math. 13(1972), 281-288 (1973; Zbl 0259.46012)]. For a Banach space X with a conjugate space \(X^*\), X is uniformly convexifiable if and only if \(X^*\) is uniformly convexifiable.