Invariant means on weakly almost periodic functionals with application to quantum groups

Abstract

Let be a Banach algebra, and let be a nonzero character on. For a closed ideal I of with such that I has a bounded approximate identity, we show that, the space of weakly almost periodic functionals on, admits a right (left) invariant -mean if and only if admits a right (left) invariant -mean. This generalizes a result due to Neufang for the group algebra as an ideal in the measure algebra, for a locally compact group G. Then we apply this result to the quantum group algebra of a locally compact quantum group. Finally, we study the existence of left and right invariant -means on. © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society.