Removed parts from Zhu citations.
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\item $\phi(1) = 1$ and $\phi(G(A)) \subset \complex \setminus \bracs{0}$.
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\end{enumerate}
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\end{theorem}
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\begin{proof}[Proof, {{\cite[Theorem I.4.5]{Zhu}}}. ]
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\begin{proof}[Proof, {{\cite[Theorem 4.5]{Zhu}}}. ]
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(1) $\Rightarrow$ (2): \autoref{proposition:multiplicative-unit}.
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(2) $\Rightarrow$ (1): Let $x \in A$ and $\lambda \in \complex$ with $|\lambda| > [x]_{sp}$, then $\lambda - x \in G(A)$ and $\phi(\lambda - x) \ne 0$. Therefore $\phi(x) \subset \ol{B(0, [x]_{sp})}$, and $\norm{\phi}_{A^*} = 1$.
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