{"paper":{"title":"Some cohomological notions on ${\\mathcal A}\\times_T {\\mathcal B}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hossein Javanshiri, Mehdi Nemati","submitted_at":"2015-09-02T22:38:28Z","abstract_excerpt":"Associated with two Banach algebras $\\mathcal A$ and $\\mathcal B$ and a norm decreasing homomorphism $T:{\\mathcal B}\\rightarrow{\\mathcal A}$, there is a certain Banach algebra product ${\\mathcal A}\\times_T {\\mathcal B}$, which is a splitting extension of $\\mathcal B$ by $\\mathcal A$. We investigate some notions of amenability such as approximate weak amenability, approximate cyclic amenability, ideal amenability, approximate Connes-amenability, Pseudo-Connes amenability, $w^*$-approximate Connes-amenability, essential amenability, essential $\\phi$-amenability and essential character amenabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00894","kind":"arxiv","version":3},"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"}