On the Embedding of von Neumann Subalgebras

Abstract:

For a von Neumann algebra with a cyclic and separating vector it will be shown that the von Neumann subalgebras with the same cyclic vector can uniquely be characterized by one-parametric operator-valued functions obeying a set of conditions. Since the properties contain no reference to the subalgebra these operator-valued functions will be called characteristic functions. On the set of characteristic functions there exists a natural topology under which this set is complete.