Definition 30.1.2 ($C^{*}$-Algebra).label Let $A$ be an involutive Banach algebra over $\complex$, then $A$ is a $C^{*}$-algebra if for every $x \in A$, $\normn{x^*x}_{A} = \norm{x}_{A}^{2}$.
Definition 30.1.2 ($C^{*}$-Algebra).label Let $A$ be an involutive Banach algebra over $\complex$, then $A$ is a $C^{*}$-algebra if for every $x \in A$, $\normn{x^*x}_{A} = \norm{x}_{A}^{2}$.
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