Let be a hypergroup. The purpose of this article is to study the question of involutions on algebras , , and . We show that the natural involution of has the canonical extension to if and only if the natural involution of has the canonical extension to . Also, we give necessary and sufficient conditions for and to admit an involution extending the natural involution of when is left amenable. Finally, we find the necessary and sufficient conditions for to admit an involution.
"Involutions in algebras related to second duals of hypergroup algebras." Ann. Funct. Anal. 8 (4) 547 - 556, November 2017. https://doi.org/10.1215/20088752-2017-0036