Definition:*-Subalgebra

Definition

Let $\struct {A, \ast}$ be a $\ast$-algebra over $\C$.

Let $B \subseteq A$ be a self-adjoint subalgebra of $A$.

We say that $B$ is a $\ast$-subalgebra of $A$.

Sources

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