We say that a Banach space $(X,\|.\|)$ has the Banach-Saks property if every bounded sequence $(x_m)_m$ in $X$ admits a subsequence $(x_{m_n})_n$ which converges in the sense of Cesàro, that is, there is a vector $x$ in $X$ such that $$ {\displaystyle \left \| {\frac {\sum_{n = 1}^{N}x_{m_{n}}}{N}} - x \right \| \underset{N}{\longrightarrow} 0.} $$ Remark
Any Banach space satisfying the Banach-Saks property is reflexive.
Question
IS the converse implication true, i.e. does every reflexive space satisfy the Banach-Saks property?
