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/