Can we find define a norm on tensor product $C(X) \otimes C(Y)$ such that the norm completion of $C(X)\otimes C(Y)=C(X\times Y)$
And can we define a norm on tensor product $L^1(X)\otimes L^1(Y)$ such that the norm completion of $L^1(X)\otimes L^1(Y)=L^1(X\times Y)$