Fully representable and *-semisimple topological partial *-algebras

J-P. Antoine; G. Bellomonte; C. Trapani

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arXiv · 1203.0509

Fully representable and -semisimple topological partial -algebras

J-P. Antoine·G. Bellomonte·C. Trapani

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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 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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BibTeX RIS

J-P. Antoine, G. Bellomonte, C. Trapani. 2012-03-02. Fully representable and *-semisimple topological partial *-algebras. https://arxiv.org/abs/1203.0509

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