{"paper":{"title":"Determinants associated to traces on operator bimodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"D. Zanin, F. Sukochev, K. Dykema","submitted_at":"2016-05-02T04:22:27Z","abstract_excerpt":"Given a II$_1$-factor $\\mathcal{M}$ with tracial state $\\tau$ and given an $\\mathcal{M}$-bimodule $\\mathcal{E}(\\mathcal{M},\\tau)$ of operators affiliated to $\\mathcal{M}$ and a trace $\\varphi$ on $\\mathcal{E}(\\mathcal{M},\\tau)$, (namely, a linear functional that is invariant under unitary conjugation), we prove that $\\det_\\varphi:\\mathcal{E}_{\\log}(\\mathcal{M},\\tau)\\to[0,\\infty)$ defined by $\\det_\\varphi(T)=\\exp(\\varphi(\\log |T|))$ is a multiplicative map on the set $\\mathcal{E}_{\\log}(\\mathcal{M},\\tau)$ of all affiliated operators $T$ such that $\\log_+(|T|)\\in\\mathcal{E}(\\mathcal{M},\\tau)$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00349","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"}