Definition:Self-Adjoint Subset of *-Algebra
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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