Fully representable and *-semisimple topological partial *-algebras
(2012) Studia Mathematica — Vol. 208, n° 2, p. 167-194 (2012)
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- Authors
Antoine, Jean-Pierre 
- 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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Antoine, J.-P., Bellomonte, G., & Trapani, C. (2012). Fully representable and *-semisimple topological partial *-algebras. Studia Mathematica, 208(2), 167-194. https://doi.org/10.4064/sm208-2-4 (Original work published 2012)