Abstract
We characterize locally convex topological algebrasA satisfying: a sequence (x n) inA converges to 0 if, and only if, (x 2 n ) converges to 0. We also show that a real Banach algebra such thatx 2 n +y 2 n →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.
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Choukri, R., El Kinani, A. & Oukhouya, A. Algébres topologiquement uniformes et algébres fortement topologiquement uniformes. Rend. Circ. Mat. Palermo 56, 235–243 (2007). https://doi.org/10.1007/BF03031442
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DOI: https://doi.org/10.1007/BF03031442