{"paper":{"title":"When do triple operator integrals take value in the trace class?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christian Le Merdy, Cl\\'ement Coine, Fedor Sukochev","submitted_at":"2017-06-06T08:59:50Z","abstract_excerpt":"Consider three normal operators $A,B,C$ on separable Hilbert space $\\H$ as well as scalar-valued spectral measures $\\lambda_A$ on $\\sigma(A)$, $\\lambda_B$ on $\\sigma(B)$ and $\\lambda_C$ on $\\sigma(C)$. For any $\\phi\\in L^\\infty(\\lambda_A\\times \\lambda_B\\times \\lambda_C)$ and any $X,Y\\in S^2(\\H)$, the space of Hilbert-Schmidt operators on $\\H$, we provide a general definition of a triple operator integral $\\Gamma^{A,B,C}(\\phi)(X,Y)$ belonging to $S^2(\\H)$ in such a way that $\\Gamma^{A,B,C}(\\phi)$ belongs to the space $B_2(S^2(\\H)\\times S^2(\\H), S^2(\\H))$ of bounded bilinear operators on $S^2(\\H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01662","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1706.01662/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}