Banach-Saks property and reflexivity On the German Wikipedia page on the Banach-Saks property, they claim that every Banach space with the Banach-Saks property is reflexive but that the converse is not true. There should be a proof due to T. Nishiura and D. Waterman, but unfortunately, I can't find a proof of this interesting statement. It would be appreciated if someone could give me an online available reference (if possible). Unfortunately, my library at the university doesn't have a copy. Thx for your help math

Here is Nishiura and Waterman's paper.

> _Nishiura, T.; Waterman, D._ , **Reflexivity and summability**, Stud. Math. 23, 53-57 (1963). ZBL0121.09402.

Albert Baernstein gives a counter-example for the converse in the paper:

> _Baernstein, Albert II_ , **On reflexivity and summability**, Stud. Math. 42, 91-94 (1972). ZBL0228.46014.