= Tomita operator
{c}
{title2=$S_0(a\Omega)=a^*\Omega$}
For a <Von Neumann algebra> with a cyclic separating <vector>, this is a densely defined antilinear operator. It is closable: the commutant orbit lies in the domain of its antilinear adjoint and is dense. Write $S$ for its <closure> and $S=J\Delta^{1/2}$ for its polar decomposition. In finite dimension it is everywhere defined and invertible. For a tracial <vector>, $S_0$ is isometric and extends to an antiunitary involution.
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