= Hilbert space module over a von Neumann algebra
{c}
= Hilbert space module
{c}
{synonym}
Here a <Hilbert space module> means a <Hilbert space> with a <unital> star-representation of a <Von Neumann algebra>, rather than a Hilbert C-star module with an algebra-valued <inner product>. A closed <invariant subspace> is reducing because the algebra is closed under adjoints. Module equivalence means an intertwining unitary. The <polar decomposition of a bounded operator> converts an intertwiner into a unitary between its initial and final support subspaces.
Back to article page
