Ideals in the dual of introverted subspaces of Ψ-pseudomeasures

2024/04/06 by Arvish Dabra, Rattan Lal, Dabra, Arvish +3 · 2 citations
Mathematics · #46J10 #46J20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A15 #Rings, Modules, and Algebras #Secondary 43A99

paper · pdf · doi:10.48550/arxiv.2404.04528

openalex publication_date 2024/04/06 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let G be a locally compact group and (Φ,Ψ) a complementary pair of Young functions satisfying the Δ₂-condition. Let A_Φ(G) be the Orlicz analogue of the Figà-Talamanca Herz algebra A_p(G). The dual of the algebra A_Φ(G) is the space of Ψ-pseudomeasures, denoted by PM_Ψ(G). For certain topologically introverted subspaces A of PM_Ψ(G) and the Banach algebras W_Φ(G) or B_Φ(G), denoted by B, we characterise the maximal regular left/right/two-sided ideals of the Banach algebras A^' and B^'' considered with the Arens product. We further characterise the minimal left ideals of A^' and prove the necessary and sufficient conditions for the existence of minimal ideals in the algebras A_Φ(G) and B.

Cited by

• Isomorphism Theorems for the Algebras of Φ-Pseudofunctions and Φ-Pseudomeasures
• Topological Center of the Double Dual of the Orlicz Figà-Talamanca Herz Algebra

Related

• Amenability and Invariant subspaces of the algebra of pseudomeasures
• Topological Center of the Double Dual of the Orlicz Figà-Talamanca Herz Algebra
• On the algebraic structures in \A_Φ(G)
• Arens regularity of the Orlicz Figà-Talamanca Herz Algebra
• Closed ideals with bounded Δ-weak approximate identities in some certain Banach algebras