{"paper":{"title":"Amalgamated duplication of the Banach algebra $\\bf{\\frak A}$ along a ${\\frak A}$-bimodule ${\\mathcal A}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hossein Javanshiri, Mehdi Nemati","submitted_at":"2016-06-11T13:44:46Z","abstract_excerpt":"Let ${\\mathcal A}$ and ${\\frak A}$ be Banach algebras such that ${\\mathcal A}$ is a Banach ${\\frak A}$-bimodule with compatible actions. We define the product ${\\cal A}\\rtimes{\\frak A}$, which is a strongly splitting Banach algebra extension of ${\\frak A}$ by $\\cal A$. After characterization of the multiplier algebra, topological centre, (maximal) ideals and spectrum of ${\\cal A}\\rtimes{\\frak A}$, we restrict our investigation to the study of semisimplicity, regularity, Arens regularity of ${\\cal A}\\rtimes{\\frak A}$ in relation to that of the algebras $\\cal A$, $\\frak A$ and the action of $\\fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03593","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"}