Definition:Unitary Element of Unital *-Algebra

Definition

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

Let $a \in A$.

Let ${\mathbf 1}_A$ be the identity element of $A$.

We say that $a$ is unitary if and only if $a^\ast a = a a^\ast = {\mathbf 1}_A$.

Sources

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