Partial \({}^*\)-algebras of closable operators. I: The basic theory and the abelian case (Q757807)

This paper is devoted to a systematic study of partial *-algebras of closable operators in a Hilbert space (partial \(Op^*\)-algebras) and to the development of a theory of representations of abstract partial *- algebras, following the pattern familiar to *-algebras. The basic theory of partial *-algebras of closable operators on a Hilbert space is reviewed. The authors also define a new kind of bounded commutant, called quasi-weak. They initiate a theory of abelian partial *-algebras and give a thorough analysis of the partial \(Op^*\)-algebras generated by a single symmetric operator and their bounded commutants.