# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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## Weakly convergent sequence coefficient of product spaceHTML articles powered by AMS MathViewer

by Guang Lu Zhang
Proc. Amer. Math. Soc. 117 (1993), 637-643 Request permission

## Abstract:

W. L. Bynum introduced the weakly convergent sequence coefficient $\operatorname {WCS} (X)$ of the Banach space $X$ as $\operatorname {WCS} (X) = {\text {sup}}\{ M:{\text {for each weakly convergent sequence}}\;\{ {x_n}\} \;{\text {in}}\;X,\;{\text {there is some }}y \in \overline {\operatorname {co} } (\{ {x_n}\} )\;{\text {such that }}M \cdot \lim \sup ||{x_n} - y|| \leqslant A(\{ {x_n}\} )\}$. 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 $\operatorname {WCS} (Z) = \min \{ \operatorname {WCS} ({X_i}):1 \leqslant i \leqslant n\}$.
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