Arens has given a way of
defining two Banach algebra products on the second dual of a Banach algebra 𝒜.
Each of these products extends the original multiplication on 𝒜 when 𝒜 is
canonically imbedded in its second dual 𝒜∗∗. In this paper we are concerned with
characterizing those Banach algebras with the property that the two Arens products
agree on the second duals.