Fully representable and *-semisimple topological partial *-algebras

Details Fully representable and *-semisimple topological partial *-algebras Fully representable and *-semisimple topological partial *-algebras

2012-03-02

arxiv.org/abs/1203.0509v1

Mathematics

Rings and Algebras

26 pages, Studia Mathematica (2012) to appear

Scientific paper

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.

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