Factorization property and Arens regularity

2010/08/16 by Kazem Haghnejad Azar, Azar, Kazem Haghnejad
Mathematics · #46L06 #46L07 #46L10 #47L25 #Advanced Topology and Set Theory #F.2.2 #FOS: Mathematics #Functional Analysis (math.FA) #I.2.7 #Rings, Modules, and Algebras #acm:46L06 #acm:46L07 #acm:46L10 #acm:47L25 #advanced mathematical theories #math.FA #msc:46L06 #msc:46L07 #msc:46L10 #msc:47L25

paper · pdf · doi:10.48550/arxiv.1008.2651

arxiv created 2010/08/16 · openalex publication_date 2010/08/16 · arxiv updated 2010/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Arens regularity properties of module actions and we extend some proposition from Baker, Dales, Lau and others into general situations. For Banach A-bimodule B, let Z₁(A^**), Z^ℓ_B^**(A^**) and Z^ℓ_A^**(B^**) be the topological centers of second dual of Banach algebra A, left module action π_ℓ:~A× B→ B and right module action π_r:~B× A→ B, respectively. We establish some relationships between them and factorization properties of A^* and B^*. We search some necessary and sufficient conditions for factorization of A^*, B and B^* with some results in group algebras. We extend the definitions of the left and right multiplier for module actions.

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