Search results for "Representable linear functional"
showing 2 items of 2 documents
Locally convex quasi *-algebras with sufficiently many *-representations
2012
AbstractThe main aim of this paper is the investigation of conditions under which a locally convex quasi ⁎-algebra (A[τ],A0) attains sufficiently many (τ,tw)-continuous ⁎-representations in L†(D,H), to separate its points. Having achieved this, a usual notion of bounded elements on A[τ] rises. On the other hand, a natural order exists on (A[τ],A0) related to the topology τ, that also leads to a kind of bounded elements, which we call “order bounded”. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi ⁎-algebras.
Extensions of representable linear functionals to unitized quasi *-algebras
2013
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 mea…