Clifford Bearden, University of Texas at Tyler
"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 $X \hookrightarrow X^{**}$ 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.
MC 5417