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arXiv · 1703.02862

Representable and continuous functionals on Banach quasi *-algebras

Maria Stella Adamo·Camillo Trapani
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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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Maria Stella Adamo, Camillo Trapani. 2017-03-08. Representable and continuous functionals on Banach quasi *-algebras. https://arxiv.org/abs/1703.02862

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