{"paper":{"title":"On commutators of compact operators via block tridiagonalization: generalizations and limitations of Anderson's approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gary Weiss, Jireh Loreaux, Sasmita Patnaik, Srdjan Petrovic","submitted_at":"2022-03-22T18:47:02Z","abstract_excerpt":"We offer a new perspective and some advances on the 1971 Pearcy--Topping problem: Is every compact operator a commutator of compact operators? Our goal is to analyze and generalize the 1970's work in this area of Joel Anderson combined with the work of the last named author of this paper. We reduce the general problem to a simpler sequence of finite matrix equations with norm constraints, while at the same time developing strategies for counterexamples. Our approach is to ask which compact operators $T$ are commutators $AB-BA$ of compact operators $A,B$; and to analyze the implications of Joel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.11995","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/2203.11995/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"}