{"paper":{"title":"n-Weak Module Amenability of Triangular Banach Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abasalt Bodaghi, Ali Jabbari","submitted_at":"2013-01-15T06:50:14Z","abstract_excerpt":"Let $\\mathcal A$, $\\mathcal B$ be Banach $\\mathfrak A$-modules with compatible actions and $\\mathcal M$ be a left Banach $\\mathcal A$-$\\mathfrak A$-module and a right Banach $\\mathcal B$-$\\mathfrak A$-module. In the current paper, we study module amenability, $n$-weak module amenability and module Arens regularity of the triangular Banach algebra $\\mathcal T=[\n{cc}\n  \\mathcal A & \\mathcal M\n  & \\mathcal B\n]$ (as an $\\mathfrak T:=\\Big{[\n{cc}\n  \\alpha &\n  & \\alpha\n] | \\alpha\\in\\mathfrak\nA\\Big}$-module). We employ these results to prove that for an inverse semigroup $S$ with subsemigroup $E$ of i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3237","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"}