{"paper":{"title":"Which traces are spectral?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"D. Zanin, F. Sukochev","submitted_at":"2013-11-05T00:56:00Z","abstract_excerpt":"Among ideals of compact operators on a Hilbert space we identify a subclass of those closed with respect to the logarithmic submajorization. Within this subclass, we answer the questions asked by Pietsch \\cite{Pietsch_nachrichten} and by Dykema, Figiel, Weiss and Wodzicki \\cite{DFWW}. In the first case, we show that Lidskii-type formulae hold for every trace on such ideal. In the second case, we provide the description of the commutator subspace associated with a given ideal. Finally, we prove that a positive trace on an arbitrary ideal is spectral if and only if it is monotone with respect to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0937","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"}