Qu^*-Algebras and Twisted Product

Abstract

Fundamental properties of Qu^*-algebras of operators are shown, and the class of CQ^*-algebras is introduced. They are the natural generalization of C^*-algebras to the case of unbounded operators. The CQ^*-algebra (\mathscr{S}₂, \mathscr{S}⁺) of distributions with the twisted product is defined, and some of their Qu^*-subalgebras are described.