Weakly convergent sequence coefficient of product space

W. L. Bynum introduced the weakly convergent sequence coefficient $\operatorname{WCS} (X)$ of the Banach space $X$ as $\operatorname{WCS} (X) = {\text{sup}}\{ M:{\text{for each weakly convergent se... ...t }}M \cdot \lim \sup \vert\vert{x_n} - y\vert\vert \leqslant A(\{ {x_n}\} )\}$. We consider the weakly convergent sequence coefficient of the ${l_p}$-product space $Z = (\prod\nolimits_{i = 1}^n {{X_i}{)_{lp}}}$ of the finite non-Schur space ${X_1}, \ldots ,{X_n}$ and show that $\operatorname{WCS} (Z) = \min \{ \operatorname{WCS} ({X_i}):1 \leqslant i \leqslant n\}$.