Let $A$ be a $C^*$-algebra.

Is it possible to characterize $A$ for which the product map defined by

$$\sum\limits_{i=1}^n a_i\otimes b_i \mapsto \sum\limits_{i=1}^n a_i b_i$$

is continuous with respect to the minimal tensor product of $C^*$-algebras?

Let $A$ be a $C^*$-algebra.

Is it possible to characterize $A$ for which the product map defined by

$$\sum\limits_{i=1}^n a_i\otimes b_i \mapsto \sum\limits_{i=1}^n a_i b_i$$

is continuous with respect to the minimal/maximal tensor product of $C^*$-algebras?