Second Duals Of Beurling Algebras

Let $A$ be a Banach algebra, with second dual space $A"$. We propose to study the space $A"$ as a Banach algebra. There are two Banach algebra products on $A"$, denoted by $\,\Box\,$ and $\,\Diamond\,$. The Banach algebra $A$ is Arens regular if the two products $\Box$ and $\Diamond$ coincide on $A"$.