# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Quasi $^*$-algebras and generalized inductive limits of $C^*$-algebras

### Tom 202 / 2011

Studia Mathematica 202 (2011), 165-190 MSC: Primary 47L60; Secondary 47L40. DOI: 10.4064/sm202-2-4

#### Streszczenie

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.

#### Autorzy

• Giorgia BellomonteDipartimento di Matematica e Informatica
Università di Palermo
I-90123 Palermo, Italy
e-mail
• Camillo TrapaniDipartimento di Matematica e Informatica
Università di Palermo
I-90123 Palermo, Italy
e-mail

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