6533b870fe1ef96bd12cf288

RESEARCH PRODUCT

Representable linear functionals on partial *-algebras

Atsushi InoueFabio BagarelloCamillo Trapani

subject

Discrete mathematicsPure mathematicsrepresentationSesquilinear formMathematics::Operator AlgebrasGeneral MathematicsSingular formMathematics - Operator AlgebrasFOS: Physical sciencesMathematical Physics (math-ph)partial *-algebrasSettore MAT/05 - Analisi Matematicapositive linear functionalFOS: MathematicsInvariant (mathematics)Mathematics::Representation TheoryOperator Algebras (math.OA)Settore MAT/07 - Fisica MatematicaMathematical PhysicsMathematics

description

A GNS-like *-representation of a partial *-algebra \({{\mathfrak A}}\) defined by certain representable linear functionals on \({{\mathfrak A}}\) is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.

yearjournalcountryeditionlanguage
2012-07-09
https://dx.doi.org/10.48550/arxiv.1207.2019