Definition:*-Algebra Homomorphism

Definition

Let $\struct {A, \ast}$ and $\struct {B, \diamond}$ be $\ast$-algebras.

Let $\phi : A \to B$ be an algebra homomorphism.

We say that $\phi$ is a $\ast$-algebra homomorphism if and only if:

$\map \phi {a^\ast} = \paren {\map \phi a}^\diamond$

for each $a \in A$.

Sources

• 1990: Gerard J. Murphy: C*-Algebras and Operator Theory ... (previous) ... (next): $2.1$: $C^\ast$-Algebras