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Volume :19 Issue : 1 1992
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Some results on weakly topologized algebras
Auther : M. AKKAR, L. OUBBI AND M. OUDADESS
Department de Mathmatiques, Ecole Normale Superieure de Takaddoum, B.P. 5118, Rabat, Maroc
ABSTRACT
We consider algebras endowed with weak topologies. We give conditions under which such algebras are locally convex. We examine the case where an algebra, endowed with a weak topology, is a locally multiplicatively convex Q-algebra and obtain that in the semi-simple case it is finite dimensional. Finally we give conditions on a locally convex algebra (E, t) under which if (E, َ(E, E)) is a locally multiplicatively convex algebra then it is of finite dimension where E is the topological dual of (E, t).