# Containment of $c_0$ in projective tensor products

Let $$X$$ and $$Y$$ be Banach spaces and denote by $$X\hat{\otimes}_\pi Y$$ the projective tensor product.

Question: If $$X\hat{\otimes}_\pi Y$$ contains an isomorphic copy of $$c_0$$, must then $$X$$ or $$Y$$ contain an isomorphic copy of $$c_0$$ also?

The answer is no. Bourgain and Pisier have given a counterexample (A construction of $$\mathcal{L}_\infty$$-spaces and related Banach spaces. Bol. Soc. Bras. Mat. 14, No. 2, 109-123 (1983). See Zbl 0586.46011 https://zbmath.org/?q=an%3A0586.46011 ).