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Quasi *-algebras and generalized inductive limits of C*-algebras

Giorgia BellomonteCamillo Trapani — 2011

Studia Mathematica

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....

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