The notion of a WCG space is a common roof for separable Banach spaces and reflexive ones. Nevertheless, the class is stable under $\ell^p(\Gamma)$-sums for any set $\Gamma$ when $p>1$ and countable $\Gamma$ when $p=1$, it is not closed under projective tensor products. More-less folklore fact states that $\ell^p(\Gamma) \hat{\otimes} \ell^p(\Gamma)$ ($\Gamma$ uncountable, $1
Is the same true for the injective tensor product? Or maybe injective tensor product of two WCG spaces is again WCG? (I think we should look for reflexive conunterexamples but I do not know any).
EDIT: Note that the natural guess $\ell^1 \otimes_\varepsilon \ell^1$ is isometrically isomorphic to $\ell^1(\ell^1)$ which is WCG.