O*-algebras in Standard System

In the previous papers [10, 12] we have defined and studied the notion of standard generalized vectors which makes possible to develop the Tomita-Takesaki theory in algebras of unbounded operators called O^*-algebras. The main purpose of this paper is to consider when an O^*-algebra is algebraically or spatially isomorphic to an O^*-algebra with a standard generalized vector.