= Von Neumann factor
{c}
{title2=$Z(M)=\mathbb CI$}
A <Von Neumann algebra> whose center consists exactly of scalar multiples of the identity. A <group von Neumann algebra> is a factor exactly when every nonidentity <conjugacy class> is infinite. A central operator has a square-summable coefficient <vector> constant on those classes; an infinite class must therefore have coefficient zero. Conversely, the sum of left translations over a finite nonidentity class is a nonscalar central operator.
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