Extensions of Representable Positive Linear Functionals to Unitized Quasi *-Algebras: A New Method

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Abstract

A topological approach for extending a representable linear functional $\omega$, defined on a topological quasi *-algebra without unit, to a representable linear functional defined on a quasi *-algebra with unit, is introduced. In particular, we suppose that $\omega$ is continuous and the positive sesquilinear form $\vom$, associated to $\omega$, is closable and prove that the extension $\overline{\vom}^e$ of the closure $\overline{\vom}$ is an i.p.s. form. By $\overline{\vom}^e$ we construct the desired extension.
Lingua originaleEnglish
pagine (da-a)997-1008
Numero di pagine12
RivistaMediterranean Journal of Mathematics
Volume12
Stato di pubblicazionePublished - 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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