The norm-strict bidual of a Banach algebra and the dual of Cu(G)

To each Banach algebra A we associate a (generally) larger Banach algebra A⁺ which is a quotient of its bidual A. It can be constructed using the strict topology on A and the Arens product on A. A⁺ has certain more pleasant properties than A, e.g. if A has a bounded right approximate identity, then A⁺ has a two-sided unit. In the special case A=L¹(G) (G a locally compact abelian group) one gets A⁺=C_u(G), the dual of the space of bounded, uniformly continuous functions on G, and we show that the center of the convolution algebra C_u(G) is precisely the space M(G) of finite measures on G.