Ternary rings of unbounded operators (Q2097363)

The authors introduce and study ternary rings of unbounded operators (TRUOs). The linking algebra of a TRUO is a pro-\(C^*\)-algebra (i.e., a complete topological \(*\)-algebra for which there exists an upward directed family of \(C^*\)-seminorms defining the topology). They prove a one-to-one correspondence between representations of a TRUO and representations of its linking pro-\(C^*\)-algebra. They study tensor products of TRUO's and show that a TRUO is Lance-nuclear if and only if its linking pro-\(C^*\)-algebra is Lance-nuclear. They propose an abstract definition of ternary pro-\(C^*\)-rings, and study their properties and their relation with TRUOs.