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On some applications of representable and continuous functionals of Banach quasi *-algebras

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arxiv 2002.08775 v1 pith:544LFZNL submitted 2020-02-18 math.FA math.OA

Maria Stella Adamo This is my paper · ORCID
classification math.FAmath.OA
keywords algebrasquasibanachfunctionalsrepresentablecontinuousrepresentabilitysome
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This survey aims to highlight some of the consequences that representable (and continuous) functionals have in the framework of Banach quasi *-algebras. In particular, we look at the link between the notions of *-semisimplicity and full representability in which representable functionals are involved. Then, we emphasize their essential role in studying *-derivations and representability properties for the tensor product of Hilbert quasi *-algebras, a special class of Banach quasi *-algebras.

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