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Locally convex quasi $C^*$-normed algebras
Fabio BagarelloCamillo TrapaniAtsushi InoueMaria Fragoulopoulousubject
Strong commutatively quasi-positive elementNormed algebraPure mathematicsApplied MathematicsRegular locally convex topologyRegular polygonStructure (category theory)Mathematics - Operator AlgebrasFOS: Physical sciencesLocally convex quasi C∗-normed algebraMathematical Physics (math-ph)Representation theoryquasi *-algebras C*-normsFunctional calculusMathematics::LogicCommutatively quasi-positive elementSettore MAT/05 - Analisi MatematicaFOS: MathematicsMultiplicationAlgebra over a fieldElement (category theory)Operator Algebras (math.OA)AnalysisMathematical PhysicsMathematicsdescription
Abstract If A 0 [ ‖ ⋅ ‖ 0 ] is a C ∗ -normed algebra and τ a locally convex topology on A 0 making its multiplication separately continuous, then A 0 ˜ [ τ ] (completion of A 0 [ τ ] ) is a locally convex quasi ∗-algebra over A 0 , but it is not necessarily a locally convex quasi ∗-algebra over the C ∗ -algebra A 0 ˜ [ ‖ ⋅ ‖ 0 ] (completion of A 0 [ ‖ ⋅ ‖ 0 ] ). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C ∗ -normed algebra, aiming at the investigation of A 0 ˜ [ τ ] ; in particular, we study its structure, ∗-representation theory and functional calculus.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-07-09 |