On the embedding of von Neumann subalgebras
Motivated by quantum field theory, the author proves the following: Given a von Neumann algebra with a cyclic and separating vector, the von Neumann subalgebras with the same cyclic vector can uniquely be characterized by ``characteristic functions'' which are one-parameter operator-valued functions fulfilling certain conditions independent on the choice of a subalgebra. Several intermediate results are leading to this final goal. The set of characteristic functions turns out to be complete under a natural topology.
scientific article; zbMATH DE number 1379905
scientific article