A module version of the weak expectation property

An operator space X is said to have the weak expectation property (WEP) if the canonical inclusion of X into its second dual factors through an injective operator space. We introduce a module version of the WEP for operator modules over completely contractive Banach algebras A. We prove many general results (for example, characterizing the A for which A-WEP implies WEP) and also focus particularly on the cases when A=L^1(G) and A=A(G) for a locally compact group G. A highlight of our work is a locally compact analogue of Lance's famous result for discrete groups that amenability is equivalent to WEP for the reduced C*-algebra. This is joint work with Jason Crann and Mehrdad Kalantar.