{"paper":{"title":"Catalysis in the trace class and weak trace class ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dmitriy Zanin, Fedor Sukochev, Guillaume Aubrun","submitted_at":"2015-06-19T12:35:32Z","abstract_excerpt":"Given operators $A,B$ in some ideal $\\mathcal{I}$ in the algebra $\\mathcal{L}(H)$ of all bounded operators on a separable Hilbert space $H$, can we give conditions guaranteeing the existence of a trace-class operator $C$ such that $B \\otimes C$ is submajorized (in the sense of Hardy--Littlewood) by $A \\otimes C$ ? In the case when $\\mathcal{I} = \\mathcal{L}_1$, a necessary and almost sufficient condition is that the inequalities ${\\rm Tr} (B^p) \\leq {\\rm Tr} (A^p)$ hold for every $p \\in [1,\\infty]$. We show that the analogous statement fails for $\\mathcal{I} = \\mathcal{L}_{1,\\infty}$ by connec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05974","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"}