Abstract
In this paper, we first show that for any Banach space $X$, $\ell_1[X]\subseteq\ell_\infty\langle X\rangle$ by Khinchin's inequality. Then by the relationship between Banach-valued sequence spaces and tensor products, we show that for any Banach space $X$, $\ell_1\stackrel{\vee}{\otimes}X\subseteq c_0\stackrel{\wedge}{\otimes}X$.
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