Housekeeping: moved von Neumann algebras to its own part.

document.tex

@@ -17,6 +17,7 @@ Occasionally, I make up some definitions to play with. These definition blocks w
 \input{./src/harmonic/index}
 \input{./src/dg/index}
 \input{./src/op/index}
+\input{./src/vna/index}
 \input{./src/dyn/index}
 %\input{./src/process/index}
 

src/op/example/index.tex

@@ -8,4 +8,3 @@
 \input{./disk.tex}
 \input{./convolution.tex}
 \input{./bc.tex}
-\input{./bb.tex}

src/op/index.tex

@@ -1,10 +1,8 @@
-\part{Operator Algebras}
+\part{Fundamentals of Operator Algebras}
 \label{part:operator-algebras}
 
 \input{./banach/index.tex}
 \input{./c-star/index.tex}
-\input{./vn/index.tex}
-\input{./ii1/index.tex}
 \input{./example/index.tex}
 \input{./system/index.tex}
 \input{./notation.tex}

src/op/notation.tex

@@ -22,7 +22,7 @@
     $(H_\phi, \pi_\phi, \xi_\phi)$ & GNS triple associated with $\phi \in S(A)$. & \autoref{definition:gns-triple} \\ 
     $L^2(M, \phi)$ & Hilbert space of the GNS triple associated with a faithful $\phi \in S(A)$. & \autoref{definition:gns-triple} \\ 
     $U(T)$ & Cayley transform of $T$. & \autoref{definition:cayley-transform-bounded} \\ 
-    $E_{x, y}$ & $E_{x, y}(B) = \dpn{E(B)x, y}{H}$. & \autoref{definition:spectral-measure} \\ 
+    $E_{x, y}$ & Section of a spectral measure $E$, where $E_{x, y}(B) = \dpn{E(B)x, y}{H}$. & \autoref{definition:spectral-measure} \\ 
     $\text{Proj}(A)$ & Projections in $A$. & \autoref{definition:vn-projection-lattice} \\
     $Z(P)$ & Central support of $P \in \text{Proj}(A)$. & \autoref{definition:central-support-vna} \\ 
     $P \sim Q$ & $P, Q \in \text{Proj}(A)$ are Murray-von Neumann equivalent & \autoref{definition:murray-von-neumann-equivalent} \\ 

src/vna/example/index.tex

@@ -0,0 +1,8 @@
+\chapter{Constructions of von Neumann Algebras}
+\label{chap:vna-example}
+
+
+\input{./bb.tex}
+\input{./lg.tex}
+\input{./hii1.tex}
+

src/vna/index.tex

@@ -0,0 +1,9 @@
+\part{Von Neumann Algebras}
+\label{part:vna}
+
+\input{./vn/index.tex}
+\input{./example/index.tex}
+\input{./ii1/index.tex}
+\input{./notation.tex}
+
+

src/vna/notation.tex

@@ -0,0 +1,13 @@
+\chapter{Notations}
+\label{chap:vna-notations}
+
+\begin{tabular}{lll}
+    \textbf{Notation} & \textbf{Description} & \textbf{Source} \\
+    \hline
+    
+    $E_{x, y}$ & Section of a spectral measure $E$, where $E_{x, y}(B) = \dpn{E(B)x, y}{H}$. & \autoref{definition:spectral-measure} \\ 
+    $\text{Proj}(A)$ & Projections in $A$. & \autoref{definition:vn-projection-lattice} \\
+    $Z(P)$ & Central support of $P \in \text{Proj}(A)$. & \autoref{definition:central-support-vna} \\ 
+    $P \sim Q$ & $P, Q \in \text{Proj}(A)$ are Murray-von Neumann equivalent & \autoref{definition:murray-von-neumann-equivalent} \\ 
+    $P \preceq Q$ & $P$ is Murray-von Neumann subequivalent to $Q$. & \autoref{definition:murray-von-neumann-subequivalent}
+\end{tabular}

src/vna/vn/index.tex

@@ -1,4 +1,4 @@
-\chapter{Von Neumann Algebras}
+\chapter{Fundamentals of von Neumann Algebras}
 \label{chap:von-neumann-algebras}
 
 \input{./topologies.tex}