Let be a hypergroup with left Haar measure and let be the complex Lebesgue space associated with it. Let be the set of all locally measurable functions that are bounded except on a locally null set, modulo functions that are zero locally a.e. It is a standard device to embed into . We denote the strong operator topology and the weak operator topology on by and . Unlike the uniform norm and weak topologies on , they depend essentially on the hypergroup structure of . We derive that the -topology is always different from the weak-topology whenever is infinite. We can conclude that for a compact hypergroup , is the dual of . The properties of and are then studied further and we pay attention to the -almost periodic elements of . Finally we give some further results about bounded linear operators which are --continuous.
"On the structure of hypergroups with respect to the induced topology." Rocky Mountain J. Math. 52 (2) 519 - 533, April 2022. https://doi.org/10.1216/rmj.2022.52.519