2010/08/16 by Kazem Haghnejad Azar, Kazem Azem Haghnejad Azar, Azar, Kazem Azem Haghnejad
Mathematics · #46L06 #46L07 #46L10 #47L25 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #F.2.2 #FOS: Mathematics #Functional Analysis (math.FA) #I.2.7 #acm:46L06 #acm:46L07 #acm:46L10 #acm:47L25 #math.FA #msc:46L06 #msc:46L07 #msc:46L10 #msc:47L25
paper · pdf · doi:10.48550/arxiv.1008.2655
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
In this paper, first we study some Arens regularity properties of module actions. Let B be a Banach A-bimodule and let Z^ℓB**(A**) and Z^ℓA**(B**) be the topological centers of the left module action π_ℓ:~A× B→ B and the right module action πr:~B× A→ B, respectively. We investigate some relationships between topological center of A**, Z1(A**) with respect to the first Arens product and topological centers of module actions Z^ℓB**(A**) and Z^ℓA**(B**). On the other hand, if A has Mazure property and B** has the left A**-factorization, then Z^ℓA**(B**)=B, and so for a locally compact non-compact group G with compact covering number card(G), we have Z^ℓM(G)**(L1(G)**)= L1(G) and Z^ℓL1(G)**(M(G)**)= M(G). By using the Arens regularity of module actions, we study some cohomological groups properties of Banach algebra and we extend some propositions from Dales, Ghahramani, Grønbæk and others into general situations and we investigate the relationships between some cohomological groups of Banach algebra A. We obtain some results in Connes-amenability of Banach algebras, and so for every compact group G, we conclude that H1w^*(L^∞(G)^*,L^∞(G)**)=0. Suppose that G is an amenable locally compact group. Then there is a Banach L1(G)-bimodule such as (L^∞(G),.) such that Z1(L1(G),L^∞(G))=\Lf:~f∈ L^∞(G)\ where for every g∈ L1(G), we have Lf(g)=f.g.