Topological Center of the Double Dual of the Orlicz Figà-Talamanca Herz Algebra

2025/05/05 by Dabra, Arvish, Kumar, N. Shravan
#43A25 #46E30 #46J10 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A15 #Secondary 43A07

paper · doi:10.48550/arxiv.2505.02474

Abstract

Let G a locally compact group and (Φ,Ψ) be a complementary pair of Young functions. Let A_Φ(G) be the Orlicz analogue of the classical Figà-Talamanca Herz algebra A_p(G). In this article, we establish a necessary and sufficient condition for the equality Λ(A_Φ(G)^∗∗) = A_Φ(G) to hold, where Λ(A_Φ(G)^∗∗) denotes the topological center of the double dual of A_Φ(G) when equipped with the first Arens product. Furthermore, we prove several results concerning the semi-simplicity of the Banach algebras A_Φ(G)^∗∗ and UCB_Ψ(\widehatG)^∗.

Citations

• Amenability and Invariant subspaces of the algebra of pseudomeasures
• Ideals in the dual of introverted subspaces of Ψ-pseudomeasures
• A modern look at algebras of operators on L^p-spaces
• Amenability and Orlicz Figa-Talamanca Herz Algebras
• Isomorphisms of Algebras of Convolution Operators

Related

• On the algebraic structures in \A_Φ(G)
• Arens regularity of the Orlicz Figà-Talamanca Herz Algebra
• Twisted Orlicz algebras, II
• Ideals in the dual of introverted subspaces of Ψ-pseudomeasures
• Amenability and Orlicz Figa-Talamanca Herz Algebras