{"paper":{"title":"Weyl's laws and Connes' Trace Theorem for operator-valued pseudo-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Edward McDonald, Xiao Xiong, Xinyu Zhang","submitted_at":"2026-05-19T01:15:49Z","abstract_excerpt":"We investigate the spectral asymptotic behavior of operator-valued classical pseudo-differential operators ($\\Psi$DOs) for negative order with symbols taking values in a semifinite von Neumann algebran $\\mathcal{M}$ equipped with a normal semifinite faithful trace. Within the framework of Connes' noncommutative geometry, we extend Connes' trace theorem to this operator-valued (type II) setting. Our main results are as follows: (i) a symbolic characterization of complex powers for operator-valued elliptic $\\Psi$DOs, extending Seeley's classical construction; (ii) a trace formula for localized R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19239","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19239/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"}