Antoine, Jean-Pierre
[UCL]
Bellomonte, Giorgia
[Università di Palermo]
Trapani, Camillo
[Università di Palermo]
We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome is that, for an appropriate order relation, one recovers the $M$-bounded elements introduced in previous works.
Bibliographic reference |
Antoine, Jean-Pierre ; Bellomonte, Giorgia ; Trapani, Camillo. Fully representable and *-semisimple topological partial *-algebras. In: Studia Mathematica, Vol. 208, no. 2, p. 167-194 (2012) |
Permanent URL |
http://hdl.handle.net/2078/125874 |