6533b86dfe1ef96bd12ca97b
RESEARCH PRODUCT
Fully representable and*-semisimple topological partial*-algebras
Jean-pierre AntoineGiorgia BellomonteCamillo Trapanisubject
Discrete mathematics*-semisimple partial *-algebrasPure mathematicsbounded elements.*-semisimple partial *-algebraGeneral MathematicsMathematics - Rings and AlgebrasTopology08A55 46K05 46K10 47L60bounded elements}topological partial *-algebrasRings and Algebras (math.RA)Settore MAT/05 - Analisi MatematicaBounded functionFOS: MathematicsInvariant (mathematics)topological partial *-algebraMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-03-02 | Studia Mathematica |