Partial \(\star\)-algebras of closable operators. II: States and representations of partial \(\star\)-algebras
This is the second paper on partial \(Op^*\)-algebras by the authors, which is devoted to the study of the theory of representations. However, the definitions for partial \(Op^*\)-algebras seem to be too general to obtain any interesting results. Therefore the authors introduce and study a subclass, called partial \(GW^*\)-algebras. The Gel'fand-Naimark-Segal (GNS) construction id given for partial \(GW^*\)-algebras. Also, for the abelian partial \(GW^*\)-algebras, they extend Power's results about the standardness of \(GNS\) representations of abelian partial \(*\)- algebras. [For part I see ibid. 26, No. 2, 359-395 (1990; Zbl 0724.47020).].
scientific article; zbMATH DE number 55942
scientific article