{"paper":{"title":"Non-commutative f-divergence functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mohammad Sal Moslehian, Mohsen Kian","submitted_at":"2013-01-30T20:18:47Z","abstract_excerpt":"We introduce the non-commutative $f$-divergence functional $\\Theta(\\widetilde{A},\\widetilde{B}):=\\int_TB_t^{\\frac{1}{2}}f\\left(B_t^{-\\frac{1}{2}} A_tB_t^{-\\frac{1}{2}}\\right)B_t^{\\frac{1}{2}}d\\mu(t)$ for an operator convex function $f$, where $\\widetilde{A}=(A_t)_{t\\in T}$ and $\\widetilde{B}=(B_t)_{t\\in T}$ are continuous fields of Hilbert space operators and study its properties. We establish some relations between the perspective of an operator convex function $f$ and the non-commutative $f$-divergence functional. In particular, an operator extension of Csisz\\'{a}r's result regarding $f$-div"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7349","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"}