Added the holomorphic functional calculus.

src/op/banach/definitions.tex

@@ -15,4 +15,14 @@
     Let $A$ be a Banach algebra, then $A$ is \textbf{unital} if there exists $1 \in A$ such that for any $x \in A$, $x1 = 1x = x$. In which case, $1$ is the unique \textbf{multiplicative identity} of $A$. 
 \end{definition}
 
+\begin{definition}[Homomorphism]
+\label{definition:banach-algebra-homomorphism}
+    Let $A, B$ be Banach algebras and $\phi: A \to B$, then $\phi$ is a \textbf{homomorphism} if:
+    \begin{enumerate}
+        \item $\phi \in L(A; B)$. 
+        \item For each $x, y \in A$, $\phi(xy) = \phi(x)\phi(y)$. 
+    \end{enumerate}
+\end{definition}
+
+