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 of A with respect to t) is a GB*-algebra. The multiplication of A[t] may be or not be jointly continuous. In the second case, Ae[t] may fail being a locally convex *-algebra, but it is a partial *-algebra. In both cases the structure and the representation theory of Ae[t] are investigated. If A[t+] denotes the t-closure of 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 *-representations of the corresponding *-algebra Ae[t].
BAGARELLO F, FRAGOULOPOULOU M, INOUE A, TRAPANI C (2006). The completion of a C*-algebra with a locally convex topology. JOURNAL OF OPERATOR THEORY, 56, 357-376.
The completion of a C*-algebra with a locally convex topology
BAGARELLO, Fabio;TRAPANI, Camillo
2006-01-01
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 of A with respect to t) is a GB*-algebra. The multiplication of A[t] may be or not be jointly continuous. In the second case, Ae[t] may fail being a locally convex *-algebra, but it is a partial *-algebra. In both cases the structure and the representation theory of Ae[t] are investigated. If A[t+] denotes the t-closure of 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 *-representations of the corresponding *-algebra Ae[t].File | Dimensione | Formato | |
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