{"paper":{"title":"On left $\\phi$-biprojectivity and left $\\phi$-biflatness of certain Banach algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Amir Sahami","submitted_at":"2019-05-14T12:31:05Z","abstract_excerpt":"In this paper, we study left $\\phi$-biflatness and left $\\phi$-biprojectivity of some Banach algebras, where $\\phi$ is a non-zero multiplicative linear function. We show that if the Banach algebra $A^{**}$ is left $\\phi$-biprojective, then $A$ is left $\\phi$-biflat. Using this tool we study left $\\phi$-biflatness of some matrix algebras. We also study left $\\phi$-biflatness and left $\\phi$-biprojectivity of the projective tensor product of some Banach algebras. We prove that for a locally compact group $G$, $M(G)\\otimes_{p} A(G)$ is left $\\phi\\otimes \\psi$-biprojective if and only if $G$ is fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05552","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"}