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Suppose that the projective tensor product of $l_{\infty}$ and $X$ contains a complemented copy of $c_{0}$. Does it follow that $X$ contains a complemented copy of $c_{0}$?

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The answer is no. In fact, by the main theorem of G. Emmanuele, "On complemented copies of $c_{0}$ in $L_{X}^p$, $1 \leq p< \infty$", Proc. Amer. Math. Soc. 104, 1988, 3, 785-786, it follows that the projective tensor product of $l_{\infty}$ and $L_{1}$ contains a complemented copy of $c_{0}$.

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