[math] \newcommand{\mathds}{\mathbb}[/math]

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Look up and learn von Neumann's reduction theory, stating that given a von Neumann algebra [math]A\subset B(H)[/math], if we write its center as

[[math]] Z(A)=L^\infty(X) [[/math]]

then we have a decomposition as follows, with the fibers [math]A_x[/math] having trivial center,

[[math]] A=\int_XA_x\,dx [[/math]]

and then write down a brief account of what you learned.