There are examples of C*-algebras A that accept a locally convex *-topology τ coarser than the given one, such that Ã[τ] (the completion of A with respect to τ) is a GB*-algebra. The multiplication of A[τ] may be or not be jointly continuous. In the second case, Ã[*] may fail being a locally convex *-algebra, but it is a partial *-algebra. In both cases the structure and the representation theory of Ã[τ] are investigated. If Ã+ τ denotes the τ-closure of the positive cone A+ of the given C*-algebra A, then the property Ā+ τ ∩ (-Ā+ τ) = {0} is decisive for the existence of certain faithful *-representations of the corresponding *-algebra Ã[τ]

BAGARELLO, F., FRAGOULOPOULOU, M., INOUE, A., TRAPANI, C. (2008). Structure of locally convex quasi C*-algebras. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 60(2), 511-549 [10.2969/jmsj/06020511].

Structure of locally convex quasi C*-algebras

BAGARELLO, Fabio;TRAPANI, Camillo
2008-01-01

Abstract

There are examples of C*-algebras A that accept a locally convex *-topology τ coarser than the given one, such that Ã[τ] (the completion of A with respect to τ) is a GB*-algebra. The multiplication of A[τ] may be or not be jointly continuous. In the second case, Ã[*] may fail being a locally convex *-algebra, but it is a partial *-algebra. In both cases the structure and the representation theory of Ã[τ] are investigated. If Ã+ τ denotes the τ-closure of the positive cone A+ of the given C*-algebra A, then the property Ā+ τ ∩ (-Ā+ τ) = {0} is decisive for the existence of certain faithful *-representations of the corresponding *-algebra Ã[τ]
2008
BAGARELLO, F., FRAGOULOPOULOU, M., INOUE, A., TRAPANI, C. (2008). Structure of locally convex quasi C*-algebras. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 60(2), 511-549 [10.2969/jmsj/06020511].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/20700
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