6533b870fe1ef96bd12cf0df
RESEARCH PRODUCT
Possible extensions of the noncommutative integral
Salvatore Triolosubject
Pure mathematicsTrace (linear algebra)General MathematicsGeneral problemSubalgebraSpace (mathematics)Noncommutative geometryLinear subspaceextensions of the noncommutative integralAlgebrasymbols.namesakeSettore MAT/05 - Analisi MatematicasymbolsAlgebra over a fieldMathematics::Representation TheoryVon Neumann architectureMathematicsdescription
In this paper we will discuss the problem of extending a trace σ defined on a dense von Neumann subalgebra \(\mathfrak{M}\) of a topological *-algebra \({\mathfrak{A}}\) to some subspaces of \({\mathfrak{A}}\). In particular, we will prove that extensions of the trace σ that go beyond the space L1(σ) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the general problem of extending positive linear functionals on a *-algebra.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-07-26 | Rendiconti del Circolo Matematico di Palermo |