Given C*-Algebras $A,B$ and $x \in A \otimes_* B$ show that:
(a) If $(\tau \otimes_* \rho)(x)=0$ for all $\tau \in A_+^*$ and $\rho \in B_+^*$, then $x=0$.
PS: $\tau \in A_+^*$ means that $\tau$ is positive functional on $A$.
(b) Can I guarantee the same result for all functional?
Anyone can help me? I'm not seeing how to use the minimality of the spatial C*-norm.
Thanks!