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?



Containment of $c_0$ in projective tensor products
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> ). 


