A generalized procedure for the construction of the inductive limit of a family of C*-algebras is proposed. The outcome is no more a C*-algebra but, under certain assumptions, a locally convex quasi *-algebra, named a C*-inductive quasi *-algebra. The properties of positive functionals and representations of C*-inductive quasi *-algebras are investigated, in close connection with the corresponding properties of positive functionals and representations of the C*-algebras that generate the structure. The typical example of the quasi *-algebra of operators acting on a rigged Hilbert space is analyzed in detail.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-2-4,
author = {Giorgia Bellomonte and Camillo Trapani},
title = {Quasi *-algebras and generalized inductive limits of C*-algebras},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {165-190},
zbl = {1220.47145},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-2-4}
}
Giorgia Bellomonte; Camillo Trapani. Quasi *-algebras and generalized inductive limits of C*-algebras. Studia Mathematica, Tome 204 (2011) pp. 165-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-2-4/