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.
Antoine, J.P., Bellomonte, G., Trapani, C. (2012). Fully representable and *-semisimple topological partial *-algebras. STUDIA MATHEMATICA, 208(2), 167-194 [10.4064/sm208-2-4].
Fully representable and *-semisimple topological partial *-algebras
BELLOMONTE, Giorgia;TRAPANI, Camillo
2012-01-01
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.File | Dimensione | Formato | |
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