Geodesic
The Second Conjugates of Certain Banach Algebras
Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 1029-1035

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a Banach algebra and A** its second conjugate space. Arens has denned two natural extensions of the product on A to A**. Under either Arens product, A** becomes a Banach algebra. Let A be a semisimple Banach algebra which is a dense two-sided ideal of a B*-algebra B and R** the radical of (A**, o). We show that A** = Q ⊕ R**, where Q is a closed two-sided ideal of A**, o). This was inspired by Alexander's recent result for simple dual A*-algebras (see [1, p. 573, Theorem 5]). We also obtain that if A is commutative, then A is Arens regular. 
Wong, Pak-Ken. The Second Conjugates of Certain Banach Algebras. Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 1029-1035. doi: 10.4153/CJM-1975-108-9
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