Abstract: 
\def\Ga{{\mit\Gamma}}
{Given a locally convex space $(V,\Ga )$, we find (all)
the multiplications $\pi$ on $V$ (associative or not) such 
 that the algebra $A\equiv (V,\pi, \Ga)$ becomes (i) $A$-convex,
(ii) $lm$-convex. 

1. Department of Mathematics
   University of Athens
   Panepistimiopolis
   Athens 15784
   Greece