The second conjugate algebras of Banach algebras (Q1321839)

Arens regularity for a Banach algebra \(A\) is defined by the identity of the two natural Arens multiplications on \(A^{**}\). The author shows, among other characterizations of Arens regularity, that, if each continuous linear map of \(A\) into \(A^*\) is weakly compact, then \(A\) is Arens regular. From this it is deduced that a \(B^*\)-algebra is Arens regular. It is also shown that a closed subalgebra inherits Arens regularity.