{"paper":{"title":"Geometry of $C^*$-algebras, the bidual of their projective tensor product, and completely bounded module maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Matthias Neufang","submitted_at":"2018-09-15T21:37:03Z","abstract_excerpt":"Let $\\mathcal{A}$ be a $C^*$-algebra, and consider the Banach algebra $\\mathcal{A} \\otimes_\\gamma \\mathcal{A}$, where $\\otimes_\\gamma$ denotes the projective Banach space tensor product; if $\\mathcal{A}$ is commutative, this is the Varopoulos algebra $V_\\mathcal{A}$. It has been an open problem for more than 35 years to determine precisely when $\\mathcal{A} \\otimes_\\gamma \\mathcal{A}$ is Arens regular. Even the situation for commutative $\\mathcal{A}$, in particular the case $\\mathcal{A} = \\ell_\\infty$, has remained unsolved. We solve this classical question for arbitrary $C^*$-algebras by usin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05772","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"}