Extensions of representable linear functionals to unitized quasi *-algebras

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Abstract

This paper starts from noting that, under certain conditions, *-representability andextensibility 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 linearfunctional defined on a quasi *-algebra $(\A,\Ao)$ without unit are given. The approach is twofold: onthe 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 theother hand a *-representable extension to the unitization of a hermitian linear functional by means of aclosable invariant sesquilinear form is constructed.
Lingua originaleEnglish
pagine (da-a)1461-1473
Numero di pagine13
RivistaMediterranean Journal of Mathematics
Volume10
Stato di pubblicazionePublished - 2013

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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