Fiest draft of nuclear operators.

src/op/c-star/gns.tex

@@ -119,7 +119,7 @@
         \phi: A \to \complex \quad x \mapsto \dpn{\pi(x)\xi, \xi}{H}
         \]
 
-        is a state on $A$. Let $(H_\phi, \pi_\phi, \xi_\phi)$ be the GNS triple associated with $\phi$, then there exists a unitary equivalence $U: H \to H_\phi$ such that $U\xi = \xi_\phi$. 
+        is a state on $A$. Moreover, if $(H_\phi, \pi_\phi, \xi_\phi)$ is the GNS triple associated with $\phi$, then there exists a unitary equivalence $U: H \to H_\phi$ such that $U\xi = \xi_\phi$. 
         \item For each $\mathcal{S} \subset S(A)$, the mapping
         \[
         \pi_{\mathcal{S}}: A \to B([l^2(\mathcal{S}); H_\phi]) \quad \pi_{\mathcal{S}}(x)(\eta)_\phi = \pi_{\phi}(x)(\eta_\phi)