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Structure of locally convex quasi C * -algebras

2008

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]

46L05quasi *-algebrasGeneral Mathematicslocally convex quasi $C^*$-algebrasRegular polygonStructure (category theory)FOS: Physical sciencesContext (language use)Mathematical Physics (math-ph)quasi-positivityCombinatoricsunbounded *-representationsMultiplicationquasi ∗-algebras quasi-positivity locally convex quasi C ∗ -algebras unbounded ∗-representations.46K10Algebra over a field46K70Settore MAT/07 - Fisica MatematicaMathematical PhysicsTopology (chemistry)47L60MathematicsJournal of the Mathematical Society of Japan
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