This paper starts from noting that, under certain conditions, *-representability and extensibility to the unitized *-algebra of a positive linear functional, defined on a *-algebra without unit, are equivalent. Here some conditions for the equivalence of the same concepts for a hermitian linear functional defined on a quasi *-algebra $(\A,\Ao)$ without unit are given. The approach is twofold: on the one hand, conditions for the equivalence are exhibited by introducing a condition for the *- representability of the extension of a *-representable functional to the unitized quasi *-algebra, on the other hand a *-representable extension to the unitization of a hermitian linear functional by means of a closable invariant sesquilinear form is constructed.
Bellomonte, G. (2013). Extensions of representable linear functionals to unitized quasi *-algebras. MEDITERRANEAN JOURNAL OF MATHEMATICS, 10(3), 1461-1473 [10.1007/s00009-013-0259-z].
Extensions of representable linear functionals to unitized quasi *-algebras
BELLOMONTE, Giorgia
2013-01-01
Abstract
This paper starts from noting that, under certain conditions, *-representability and extensibility to the unitized *-algebra of a positive linear functional, defined on a *-algebra without unit, are equivalent. Here some conditions for the equivalence of the same concepts for a hermitian linear functional defined on a quasi *-algebra $(\A,\Ao)$ without unit are given. The approach is twofold: on the one hand, conditions for the equivalence are exhibited by introducing a condition for the *- representability of the extension of a *-representable functional to the unitized quasi *-algebra, on the other hand a *-representable extension to the unitization of a hermitian linear functional by means of a closable invariant sesquilinear form is constructed.File | Dimensione | Formato | |
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