ON THE STATISTICAL INDEPENDENCE OF ALGEBRAS OF OBSERVABLES

We reexamine various notions of statistical independence presently in use in algebraic quantum theory, establishing alternative characteriza tions for such independence, some of which are also valid without assu ming that the observable algebras mutually commute. In addition, in th e context which holds in concrete applications to quantum theory, the equivalence of three major notions of statistical independence is prov en. (C) 1997 American Institute of Physics.