LINEAR OPERATORS WHICH COMMUTE WITH TRANSLATIONS

Let G be a locally compact group and let ¡ be a closed subgroup of G£G. In this talk, the concept of commutativity with respect to a closed subgroup of a product group, which is a generalization of multipliers under the usual sense, will be introduced. As a consequence, we obtain the characterization of operators on L2(G) which commute with left translation when G is amenable as discrete.