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.

Adamo, M., Trapani, C. (2017). Representable and Continuous Functionals on Banach Quasi *-Algebras. MEDITERRANEAN JOURNAL OF MATHEMATICS, 14(4) [10.1007/s00009-017-0957-z].

Representable and Continuous Functionals on Banach Quasi *-Algebras

ADAMO, MARIA STELLA;TRAPANI, Camillo
2017-01-01

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.
2017
http://springerlink.metapress.com/app/home/journal.asp?wasp=46wluhqumg3vd7j5nre7&referrer=parent&backto=browsepublicationsresults,355,537;
Adamo, M., Trapani, C. (2017). Representable and Continuous Functionals on Banach Quasi *-Algebras. MEDITERRANEAN JOURNAL OF MATHEMATICS, 14(4) [10.1007/s00009-017-0957-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/245030
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