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Displaying similar documents to “States and representations of CQ*-algebras”

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

Giorgia Bellomonte, Camillo Trapani (2011)

Studia Mathematica

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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...

C*-seminorms on partial *-algebras: an overview

Camillo Trapani (2005)

Banach Center Publications

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The main facts about unbounded C*-seminorms on partial *-algebras are reviewed and the link with the representation theory is discussed. In particular, starting from the more familiar case of *-algebras, we examine C*-seminorms that are defined from suitable families of positive linear or sesquilinear forms, mimicking the construction of the Gelfand seminorm for Banach *-algebras. The admissibility of these forms in terms of the (unbounded) C*-seminorms they generate is characterized. ...