{"paper":{"title":"Cartan subalgebras of operator ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Daniel Beltita, Gary Weiss, Sasmita Patnaik","submitted_at":"2014-08-21T06:39:33Z","abstract_excerpt":"Denote by $U_{\\mathcal I}({\\mathcal H})$ the group of all unitary operators in ${\\bf 1}+{\\mathcal I}$ where ${\\mathcal H}$ is a separable infinite-dimensional complex Hilbert space and ${\\mathcal I}$ is any two-sided ideal of ${\\mathcal B}({\\mathcal H})$. A Cartan subalgebra ${\\mathcal C}$ of ${\\mathcal I}$ is defined in this paper as a maximal abelian self-adjoint subalgebra of~${\\mathcal I}$ and its conjugacy class is defined herein as the set of Cartan subalgebras $\\{V{\\mathcal C} V^*\\mid V\\in U_{\\mathcal I}({\\mathcal H})\\}$. For nonzero proper ideals ${\\mathcal I}$ we construct an uncounta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4897","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"}