Invariant means on a class of von Neumann algebras

Abstract

For G a locally compact group with associated von Neumann algebra VN(G) we prove the existence of an invariant mean on VN(G).This mean is shown to be unique if and only if G is discrete.It follows readily that VN(G) is an A(G>module and that ||zzT|| < |||| ||T||.A linear functional 722 on VN(G) is called a 7Z2ea72 if