{"paper":{"title":"Approximate biprojectivity and $\\phi$-biflatness of certain Banach algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Pourabbas, A. Sahami","submitted_at":"2014-09-26T09:09:07Z","abstract_excerpt":"In this paper we are going to investigate the approximate biprojectivity and the $\\phi$-biflatness of some Banach algebras related to the locally compact groups. We show that a Segal algebra $S(G)$ is approximate biprojective if and only if $G$ is compact. Also for a continuous weight $w\\geq 1$, we show that $L^{1}(G,w)$ is a approximate biprojective if and only if $G$ is compact. We study $\\phi$-biflatness of some Banach algebras, where $\\phi:A\\rightarrow \\mathbb{C}$ is a multiplicative linear functional. We show that if $S(G)$ is $\\phi$-biflat, then $G$ is amenable group. Also we show that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7503","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"}