The completion of a (normed) -algebra with respect to a locally convex topology on that makes the multiplication of separately continuous is, in general, a quasi -algebra, and not a locally convex -algebra , . In this way, one is led to consideration of locally convex quasi -algebras, which generalize -algebras in the context of quasi -algebras. Examples are given and the structure of these relatives of -algebras is investigated.
Fabio BAGARELLO. Maria FRAGOULOPOULOU. Atsushi INOUE. Camillo TRAPANI. "Structure of locally convex quasi -algebras." J. Math. Soc. Japan 60 (2) 511 - 549, April, 2008. https://doi.org/10.2969/jmsj/06020511