Added section regarding the duality of L^p spaces.

src/fa/norm/hilbert.tex

@@ -352,7 +352,7 @@ A significant property of Hilbert spaces is that every closed subspace is comple
     \phi_x: H \to \complex \quad \phi_x(y) = \dpn{y, x}{E}
     \]
 
-    then the mapping $H \to H^*$ defined by $x \mapsto \phi_x$ is an isometric conjugate linear isomorphism. 
+    then the mapping $H \to H^*$ defined by $x \mapsto \phi_x$ is an conjugate linear isometric isomorphism. 
 \end{theorem}
 \begin{proof}
     By the \hyperref[Cauchy-Schwarz inequality]{proposition:cauchy-schwarz} and definition of the norm, $x \mapsto \phi_x$ is an isometric conjugate linear map. 

src/fa/norm/separable.tex

@@ -6,7 +6,7 @@
     Let $K \in \RC$ and $\dpn{E, F}{\lambda}$ be a duality of normed vector spaces over $K$ with $E$ being separable, then
     \begin{enumerate}
         \item The closed unit ball $S = \bracsn{y \in F|\ \norm{y}_{F} \le 1}$ is separable with respect to the $\sigma(F, E)$-topology. 
-        \item If the duality is norming, then there exists $\seq{y_n} \subset F$ such that for each $x \in E$, $\norm{x}_E = \sup_{n \in \natp}\dpn{x, y_n}{\lambda}$. 
+        \item If the duality is norming, then there exists $\seq{y_n} \subset F$ such that for each $x \in E$, $\norm{x}_E = \sup_{n \in \natp}|\dpn{x, y_n}{\lambda}|$. 
     \end{enumerate}
 \end{proposition}
 \begin{proof}