Fixed regex incident.
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This commit is contained in:
Bokuan Li
2026-05-05 02:00:05 -04:00
parent 0f2e69d1f9
commit 97372173e1
78 changed files with 172 additions and 172 deletions

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@@ -38,13 +38,13 @@
\begin{enumerate}
\item[(a)] $\norm{x}_E \le C\norm{y}_F$.
\item[(b)] $\norm{y - Tx}_F \le \gamma \norm{y}_F$.
\end\{enumerate\}
\end{enumerate}
then for any $y \in F$, there exists $\seq{x_n} \subset E$ such that:
\begin{enumerate}
\item $\sum_{n \in \natp}\norm{x_n}_E \le C\norm{y}_F/(1 - \gamma)$.
\item $\sum_{n = 1}^\infty Tx_n = y$.
\end\{enumerate\}
\end{enumerate}
In particular, if $E$ is a Banach space, then for every $y \in F$, there exists $x \in E$ such that $\norm{x}_E \le C\norm{y}_F/(1 - \gamma)$ and $Tx = y$.
\end{theorem}
@@ -75,7 +75,7 @@
\begin{enumerate}
\item For every $x \in E$, $\sup_{T \in \mathcal{T}}\norm{Tx}_F < \infty$.
\item $E$ is a Banach space.
\end\{enumerate\}
\end{enumerate}
then $\sup_{T \in \mathcal{T}}\norm{T}_{L(E; F)} < \infty$.
\end{theorem}