Algébres topologiquement uniformes et algébres fortement topologiquement uniformes

摘要

We characterize locally convex topological algebrasA satisfying: a sequence (x n) inA converges to 0 if, and only if, (x n 2 ) converges to 0. We also show that a real Banach algebra such thatx n 2 +y n 2 →0 if, and only if,x n → 0 andy n → 0, for every sequences (x n) and (y n) inA, is isomorphic to $C_mathbb{R} (X)$ , whereX is a compact space.