Non-commutative -spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (,₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-3-6,
author = {Fabio Bagarello and Camillo Trapani and Salvatore Triolo},
title = {Quasi *-algebras of measurable operators},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {289-305},
zbl = {1101.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-3-6}
}
Fabio Bagarello; Camillo Trapani; Salvatore Triolo. Quasi *-algebras of measurable operators. Studia Mathematica, Tome 173 (2006) pp. 289-305. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-3-6/