jerrylicious/garden
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Fixed typo in Hahn-Banach.

Browse Source
This commit is contained in:
Bokuan Li
2026-03-19 19:26:43 -04:00
parent 9ce4986002
commit 051bae6096
1 changed files with 1 additions and 1 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
src/fa/lc/hahn-banach.tex
View File

@@ -37,7 +37,7 @@
\begin{theorem}[Hahn-Banach, Analytic Form {{\cite[Theorem 5.6, 5.7]{Folland}}}]
\label{theorem:hahn-banach}
Let $E$ be a vector space over $K \in \RC$, $\rho: E \to \real$ be a sublinear functional, $F \subsetneq E$ be a subspace,
Let $E$ be a vector space over $K \in \RC$, $\rho: E \to \real$ be a sublinear functional, and $F \subsetneq E$ be a subspace, then
\begin{enumerate}
\item For any $\phi \in \hom(F; \real)$ with $\phi \le \rho|_F$, there exists $\Phi \in \hom(E; \real)$ such that $\Phi \le \rho$ and $\Phi|_F = \phi$.
\item If $\rho$ is a seminorm, then for any $\phi \in \hom(F; \complex)$ with $\abs{\phi} \le \rho|_F$, there exists $\Phi \in \hom(E; \complex)$ such that $\abs{\Phi} \le \rho$ and $\Phi|_F = \phi$.