Spatial theory for algebras of unbounded operators

Abstract

In this paper, the spatial theory of ^∗-automorphisms is investigated in the context of algebras of unbounded operators. In particular, it is shown that ^∗-automorphisms, satisfying some order relation, of the Op^∗-algebra generated by the position and momentum operators q_j, p_j(j=1,...., n) on the Schwartz space $\text{I}\text{(}\text{R}{}^{\mathrm{n}}\text{)}$ are unitarily implemented.