Removed parts from Zhu citations.

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Bokuan Li
2026-07-07 11:39:54 -04:00
parent 86aba8ee4b
commit f613e65d10
11 changed files with 17 additions and 10 deletions

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@@ -69,7 +69,7 @@
\item $\phi(1) = 1$ and $\phi(G(A)) \subset \complex \setminus \bracs{0}$.
\end{enumerate}
\end{theorem}
\begin{proof}[Proof, {{\cite[Theorem I.4.5]{Zhu}}}. ]
\begin{proof}[Proof, {{\cite[Theorem 4.5]{Zhu}}}. ]
(1) $\Rightarrow$ (2): \autoref{proposition:multiplicative-unit}.
(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 $\norm{\phi}_{A^*} = 1$.