Added setup for GNS.

src/op/banach/definitions.tex

@@ -29,9 +29,16 @@
 
 \begin{definition}[Unital Homomorphism]
 \label{definition:banach-algebra-unital-homomorphism}
-    Let $A, B$ be unital Banach algebras and $\phi: A \to B$ be a homomorphism, then $\phi$ is a \textbf{unital homomorphism} if $\phi(1) = 1$. 
+    Let $A, B$ be unital Banach algebras and $\phi: A \to B$ be a homomorphism, then $\phi$ is a \textbf{unital homomorphism} if $\phi(1_A) = 1_B$. 
 \end{definition}
 
+\begin{definition}[Representation]
+\label{definition:banach-algebra-representation}
+    Let $A$ be a Banach algebra, then a \textbf{representation} of $A$ is a pair $(E, \pi)$ where $E$ is a Banach space, and $\pi: A \to L(E; E)$ is a continuous homomorphism. 
+\end{definition}
+
+
+
 \begin{definition}[Unitisation]
 \label{definition:unitisation}
     Let $A$ be a Banach algebra over $\complex$, and $\tilde A = \complex \oplus A$ with