{"paper":{"title":"Factorization property and Arens regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kazem Haghnejad Azar","submitted_at":"2010-08-16T13:29:33Z","abstract_excerpt":"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 $Z_1(A^{**})$, ${Z}^\\ell_{B^{**}}(A^{**})$ and ${Z}^\\ell_{A^{**}}(B^{**})$ be the topological centers of second dual of Banach algebra $A$, left module action $\\pi_\\ell:~A\\times B\\rightarrow B$ and right module action $\\pi_r:~B\\times A\\rightarrow B$, respectively. We establish some relationships between them and factorization properties of $A^*$ and $B^*$. We search some necessary and sufficient cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2651","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}