Г-invariant operators associated with locally compact groups

Abstract

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