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\end{proof}
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\begin{definition}[Absolute Value]
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\label{definition:absolute-value-c-star}
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Let $A$ be a $C^*$-algebra and $x \in A$, then $|x| = \sqrt{x^*x}$ is the \textbf{absolute value} of $x$. If $x$ is self-adjoint, then $|x| =
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\end{definition}
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