Definition 41.6.4 (Conditional Expectation).label Let $A, B$ be unital $C^{*}$-algebras and $\phi: A \to B$ be a linear map, then $\phi$ is a conditional expectation if:
- (1)
$\phi$ is unital and completely positive.
- (2)
$\phi|_{B}$ is the identity.
Definition 41.6.4 (Conditional Expectation).label Let $A, B$ be unital $C^{*}$-algebras and $\phi: A \to B$ be a linear map, then $\phi$ is a conditional expectation if:
$\phi$ is unital and completely positive.
$\phi|_{B}$ is the identity.
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