On m-convexity of commutative real Waelbroeck algebras

We prove that the complexification of a commutative real Waelbroeck algebra is again such an algebra, and apply this result for showing that a commutative real locally convex Prechet Q-algebra must be m-convex, and, more generally, a commutative real locally convex Waelbroeck algebra must be m-convex. In this way we extend onto the real case two results known in the complex case and thus solve a problem posed in [9].