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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-2-4,
author = {J.-P. Antoine and G. Bellomonte and C. Trapani},
title = {Fully representable and *-semisimple topological partial *-algebras},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {167-194},
zbl = {1238.47050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-2-4}
}
J.-P. Antoine; G. Bellomonte; C. Trapani. Fully representable and *-semisimple topological partial *-algebras. Studia Mathematica, Tome 209 (2012) pp. 167-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-2-4/