Fully representable and *-semisimple topological partial *-algebras

• Autorzy: J.-P. Antoine , G. Bellomonte , C. Trapani
• Języki publikacji: EN

Abstrakty

EN

We continue our study of topological partial *-algebras, focusing our attention on *-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 aim 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.

Kategorie tematyczne

• 47L60: Algebras of unbounded operators; partial algebras of operators
• 46K10: Representations of topological algebras with involution
• 08A55: Partial algebras
• 46K05: General theory of topological algebras with involution

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 208
• Numer: 2
• Strony: 167-194

Daty

wydano

2012

Twórcy

autor

J.-P. Antoine

• Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

autor

G. Bellomonte

• Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo, Italy

autor

C. Trapani

• Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo, Italy

Identyfikatory

DOI

10.4064/sm208-2-4