# The completion of a C*-algebra with a locally convex topology

Camillo Trapani, Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue

Risultato della ricerca: Article

7 Citazioni (Scopus)

### Abstract

There are examples of C*-algebras A that accept a locally convex*-topology t coarser than the given one, such that Ae[t] (the completion ofA with respect to t) is a GB*-algebra. The multiplication of A[t] may be ornot be jointly continuous. In the second case, Ae[t] may fail being a locallyconvex *-algebra, but it is a partial *-algebra. In both cases the structure andthe representation theory of Ae[t] are investigated. If A[t+]denotes the t-closureof the positive cone A+ of the given C*-algebra A, then the property A[t]+\cap (−A[t]+) = {0} is decisive for the existence of certain faithful *-representationsof the corresponding *-algebra Ae[t].
Lingua originale English 357-376 20 JOURNAL OF OPERATOR THEORY 56 Published - 2006

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C*-algebra
Completion
Topology
Algebra
Partial Algebra
Positive Cone
Faithful
Representation Theory
Property A
Multiplication
Denote
Cap

### All Science Journal Classification (ASJC) codes

• Algebra and Number Theory

### Cita questo

The completion of a C*-algebra with a locally convex topology. / Trapani, Camillo; Bagarello, Fabio; Fragoulopoulou, Maria; Inoue, Atsushi.

In: JOURNAL OF OPERATOR THEORY, Vol. 56, 2006, pag. 357-376.

Risultato della ricerca: Article

Trapani, Camillo ; Bagarello, Fabio ; Fragoulopoulou, Maria ; Inoue, Atsushi. / The completion of a C*-algebra with a locally convex topology. In: JOURNAL OF OPERATOR THEORY. 2006 ; Vol. 56. pagg. 357-376.
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AB - There are examples of C*-algebras A that accept a locally convex*-topology t coarser than the given one, such that Ae[t] (the completion ofA with respect to t) is a GB*-algebra. The multiplication of A[t] may be ornot be jointly continuous. In the second case, Ae[t] may fail being a locallyconvex *-algebra, but it is a partial *-algebra. In both cases the structure andthe representation theory of Ae[t] are investigated. If A[t+]denotes the t-closureof the positive cone A+ of the given C*-algebra A, then the property A[t]+\cap (−A[t]+) = {0} is decisive for the existence of certain faithful *-representationsof the corresponding *-algebra Ae[t].

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JO - JOURNAL OF OPERATOR THEORY

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