Fully representable and *-semisimple topological partial *-algebras

Camillo Trapani, Giorgia Bellomonte, Jean-Pierre Antoine

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6 Citazioni (Scopus)

Abstract

We continue our study of topological partial *-algebras, focusingour attention to *-semisimple partial *-algebras, that is, those that possessa multiplication core and su ciently many *-representations. We discuss therespective roles of invariant positive sesquilinear (ips) forms and representablecontinuous linear functionals and focus on the case where the two notions arecompletely interchangeable (fully representable partial *-algebras) with thescope of characterizing a *-semisimple partial *-algebra. Finally we describevarious notions of bounded elements in such a partial *-algebra, in particular,those defined in terms of a positive cone (order bounded elements). The outcomeis that, for an appropriate order relation, one recovers the M-boundedelements introduced in previous works.
Lingua originaleEnglish
pagine (da-a)167-194
Numero di pagine28
RivistaStudia Mathematica
Volume208
Stato di pubblicazionePublished - 2012

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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