Let $A$ be a C*-algebra. Then there exists a net $(e_i)_{i\in \Lambda}$ in $A$ such that, for every $i\in \Lambda$, the element $e_i$ is positive and satisfies $\|e_i\|_A\le 1$, and for every $a\in A$,
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\begin{align*}
\|ae_i-a\|_A \to 0
\end{align*}
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and
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\begin{align*}
\|e_i a-a\|_A \to 0.
\end{align*}
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More generally, if $I\trianglelefteq A$ is a closed two-sided ideal, then $I$, with its inherited C*-algebra structure, has a contractive positive approximate identity contained in $I$.