Example 41.3.12.label Let $A, B$ be $C^{*}$-algebras and $\phi: A \to B$ be a *-homomorphism, then $\phi$ is completely positive.
Proof. For each $n \in \natp$, the induced map $\phi_{n}: M_{n}(A) \to M_{n}(B)$ is a *-homomorphism.$\square$
Example 41.3.12.label Let $A, B$ be $C^{*}$-algebras and $\phi: A \to B$ be a *-homomorphism, then $\phi$ is completely positive.
Proof. For each $n \in \natp$, the induced map $\phi_{n}: M_{n}(A) \to M_{n}(B)$ is a *-homomorphism.$\square$
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