OPERATORS WHICH COMMUTE WITH THE CONJUGATE CONVOLUTION OPERATIONS

Let G be a locally compact group with a fixed left Haar measure lambda. Let L-infinity (G), L-1 (G) be the usual Lebesgue spaces with respect to lambda. In this paper, we show that there is an isometric homomorphism from U-infinity (G)* into the set of all bounded linear operators on L-infinity (G) which commute with conjugate convolution, where U-infinity (G) is the subspace of L-infinity (G) consisting of all f is an element of L-infinity (G) for which the mapping y -> (y-1)f(y) from G into L-infinity (G) is continuous.