Various typo fixes.
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Bokuan Li
2026-05-30 20:35:32 -04:00
parent 0cea712b96
commit edde66facc
3 changed files with 4 additions and 4 deletions

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@@ -80,7 +80,7 @@
then $\sup_{T \in \mathcal{T}}\norm{T}_{L(E; F)} < \infty$.
\end{theorem}
\begin{proof}
By the \autoref{theorem:banach-steinhaus} theorem, $\mathcal{T}$ is equicontinuous. Therefore there exists $r > 0$ such that $\bigcup_{T \in \mathcal{T}}T[B_E(0, r)] \subset B_F(0, 1)$. In which case, $\sup_{T \in \mathcal{T}}\norm{T}_{L(E; F)} \le r^{-1}$.
By the \hyperref[Banach-Steinhaus Theorem]{theorem:banach-steinhaus}, $\mathcal{T}$ is equicontinuous. Therefore there exists $r > 0$ such that $\bigcup_{T \in \mathcal{T}}T[B_E(0, r)] \subset B_F(0, 1)$. In which case, $\sup_{T \in \mathcal{T}}\norm{T}_{L(E; F)} \le r^{-1}$.
\end{proof}