Let H be a locally compact hypergroup with left Haar measure and let LUC(H) be the collection of left uniformly continuous functions on H. Two new topologies \(\tau _1\) and \(\tau _2\) are introduced on \(LUC(H)^*\) . We study these topologies and compare them with each other and with the norm and \(\hbox {weak}^*\) -topologies. For a commutative compact hypergroup H, we deduce that \(\tau _1\) -topology is different from the norm-topology on \(LUC(H)^*\) whenever H is infinite. As another result, we deduce that \(\tau _1\) is different from the \(\hbox {weak}^*\) -topology on \(LUC(H)^*\) whenever H is non-compact. The properties of \(\tau _1\) are then studied further and we pay attention to commutant operators on \(LUC(H)^*\) . Finally we give some further results about \(\tau _1\) -continuous operators on \(LUC(H)^*\) .
