Representable and continuous functionals on Banach quasi *-algebras

2017/03/08 by Maria Stella Adamo, Adamo, Maria Stella, Camillo Trapanı +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1703.02862

openalex publication_date 2017/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Eigenstates of CQ*-algebras

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