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GIORGIA BELLOMONTE

Fully representable and *-semisimple topological partial *-algebras

  • Autori: Antoine, JP; Bellomonte, G; Trapani, C
  • Anno di pubblicazione: 2012
  • Tipologia: Articolo in rivista (Articolo in rivista)
  • Parole Chiave: topological partial *-algebras; *-semisimple partial *-algebras; bounded elements.
  • OA Link: http://hdl.handle.net/10447/62970

Abstract

We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a multiplication core and su ciently 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.