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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@@ -42,7 +42,7 @@
\label{proposition:unitary-spectrum}
Let $A$ be a unital $C^*$-algebra and $x \in A$ be unitary, then $\sigma_A(x) \subset \partial B_\complex(0, 1)$.
\end{proposition}
\begin{proof}[Proof, {{\cite[Proposition II.8.2]{Zhu}}}. ]
\begin{proof}[Proof, {{\cite[Proposition 8.2]{Zhu}}}. ]
By \autoref{lemma:unitary-unit}, $\norm{x}_A = 1$, so $\sigma_A(x) \subset \ol{B_\complex(0, 1)}$. Thus
\[
\bracsn{\ol{\lambda}|\lambda \in \sigma_A(x)} = \sigma_A(x^*) = \sigma_A(x^{-1}) \subset \ol{\complex \setminus B_\complex(0, 1)}