2025/12/09 by Sababe, Saeed Hashemi
Mathematics · #43A20 #46B20 #46H20 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary 43A62 #Random Matrices and Applications #Secondary 43A15
paper · pdf · doi:10.48550/arxiv.2512.09955
openalex publication_date 2025/12/09 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28
We investigate the Arens products on the second duals of convolution algebras associated with Chébli--Trimèche hypergroups, particularly focusing on the left and right topological centres of L1(H)′′ and M(H)′′. Building on the recent framework established by Losert, we relax the classical smoothness assumptions on the underlying Sturm--Liouville function A and develop new asymptotic analysis tools for measure-valued and low-regularity perturbations. This allows us to extend the existence and continuity of the asymptotic measures νx and the limit measure ν∞ to a strictly larger class of hypergroups. We further provide new necessary and sufficient conditions for strong Arens irregularity of L1(H) in terms of the spectral behaviour of ν∞, explore weighted (Beurling-type) hypergroup algebras, and obtain the first detailed comparison between the left and right topological centres for a wide class of non-classical examples. Several concrete applications to Jacobi, Naimark, and Bessel--Kingman hypergroups are presented.