A question about minimal tensor product

79 Views Asked by At

Let $A$ and $B_n$ be C*-algebras. we can define a *-homomorphism $\pi: A\otimes( \Pi_{n} B_n)\to\Pi_{n} (A\otimes B_n) $ be $\pi(a\otimes(b_n)_n)=(a\otimes b_n)_n$, where $a\in A$ and $b_n\in B_n$($\otimes$ is minimal tensor product,). How to understand $\pi$ is not surjective if A is infinite dimensional? Please help me!