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Weakly convergent sequence coefficient of product space


Author: Guang Lu Zhang
Journal: Proc. Amer. Math. Soc. 117 (1993), 637-643
MSC: Primary 46B45
DOI: https://doi.org/10.1090/S0002-9939-1993-1152993-1
MathSciNet review: 1152993
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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 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\} $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1152993-1
Keywords: Asymptotic equidistant sequence, weakly convergent sequence coefficient
Article copyright: © Copyright 1993 American Mathematical Society

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