Definition 41.3.2 (Extended Map).label Let $A$ be a unital $C^{*}$-algebra, $B$ be a $C^{*}$-algebra, $S \subset A$ be an operator system, $\phi: S \to B$ be a linear map, and $n \in \natp$, then the mapping
\[\phi_{n} = \text{Id}_{M_n(\complex)}\otimes \phi: M_{n}(S) \to M_{n}(B)\]
is the extended map/amplification of $\phi$ to $M_{n}(S)$.
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