We continue our study of topological partial *-algebras, focusing on the interplay between various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between strong and weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *-algebras, emphasizing the crucial role played by appropriate bounded elements, called ℳ-bounded. Finally, some remarks are made concerning representations in terms of so-called partial GC*-algebras of operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-3-2,
author = {Jean-Pierre Antoine and Camillo Trapani and Francesco Tschinke},
title = {Bounded elements in certain topological partial *-algebras},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {223-251},
zbl = {1221.47145},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-3-2}
}
Jean-Pierre Antoine; Camillo Trapani; Francesco Tschinke. Bounded elements in certain topological partial *-algebras. Studia Mathematica, Tome 204 (2011) pp. 223-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-3-2/