{"paper":{"title":"On homological notions of Banach algebras related to a character","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Sahami","submitted_at":"2014-01-11T19:40:30Z","abstract_excerpt":"In this paper, we countinue our work in \\cite{11}.\n  We show that $L^{1}(G,w)$ is $\\phi_{0}$-biprojective if and only if $G$ is compact, where $\\phi_{0}$ is the augmentation character. We introduce the notions of character Johnson amenability and character Johnson contractibility for Banach algebras. We show that $\\ell^{1}(S)$ is pseudo-amenable if and only if $\\ell^{1}(S)$ is character Johnson-amenable, provided that $S$ is a uniformly locally finite band semigroup.\n  We give some conditions whether $\\phi$-biprojectivity ($\\phi$-biflatness) of $\\ell^{1}(S)$ implies the finiteness (amenability"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2558","kind":"arxiv","version":2},"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"}