Standard weights on algebras of unbounded operators

Abstract

The purpose of this paper is to define and study an important class in weights on $O^{*}$-algebras which is possible to develop the Tomita-Takesaki theory in $O^{*}$-algebras. The Connes cocycle theorem for weights on von Neumann algebras is generalized to the case of $O^{*}$-algebras.