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

Abstract

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.

Contribution Proceedings of the International Workshop on Operator Theory and its Applications (IWOTA) 2019, Lisbon. arXiv admin note: text overlap with arXiv:1809.00470