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

• Autorzy: Giorgia Bellomonte , Camillo Trapani
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L60: Algebras of unbounded operators; partial algebras of operators
• 47L40: Limit algebras, subalgebras of C * -algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 202
• Numer: 2
• Strony: 165-190

Daty

wydano

2011

Twórcy

autor

Giorgia Bellomonte

• Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo, Italy

autor

Camillo Trapani

• Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo, Italy

Identyfikatory

DOI

10.4064/sm202-2-4