Representable and Continuous Functionals on Banach Quasi *-Algebras

Camillo Trapani, Maria Stella Adamo

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1 Citazioni (Scopus)

Abstract

In the study of locally convex quasi *-algebras an important role is played by representable linear functionals, i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved.
Lingua originaleEnglish
Numero di pagine25
RivistaMediterranean Journal of Mathematics
Volume14
Stato di pubblicazionePublished - 2017

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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