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Representable and Continuous Functionals on Banach Quasi *-Algebras

2017

In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved.

Banach quasi *-algebraGeneral MathematicsHilbert quasi01 natural sciencesRepresentable functionalsAutomatic continuity of representable functional0103 physical sciencesFOS: MathematicsMathematics (all)Banach quasi0101 mathematicsOperator Algebras (math.OA)MathematicsDiscrete mathematics010102 general mathematicsMathematics - Operator AlgebrasRegular polygonAutomatic continuity of representable functionalsFunctional Analysis (math.FA)Mathematics - Functional AnalysisAutomatic continuity of representable functionals; Banach quasi; Hilbert quasi; Representable functionals; MathematicsRepresentable functionalBounded functionHilbert quasi *-algebra010307 mathematical physicsMathematicsMediterranean Journal of Mathematics
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