Definition:Self-Adjoint Subset of *-Algebra

Definition

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

Let $S \subseteq A$ be a subset of $A$ such that:

for each $a \in S$ we have $a^\ast \in S$.

We say that $S$ is a self-adjoint subset of $A$.

Sources

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