{"paper":{"title":"Ergodic theorems in Banach ideals of compact operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Aziz Azizov, Semyon Litvinov, Vladimir Chilin","submitted_at":"2019-02-02T18:13:34Z","abstract_excerpt":"Let $\\mathcal H$ be an infinite-dimensional Hilbert space, and let $\\mathcal B(\\mathcal H)$ ($\\mathcal K(\\mathcal H)$) be the $C^*$-algebra of bounded (respectively, compact) linear operators in $\\mathcal H$. Let $(E,\\|\\cdot\\|_E)$ be a fully symmetric sequence space. If $\\{s_n(x)\\}_{n=1}^\\infty$ are the singular values of $x\\in\\mathcal K(\\mathcal H)$, let $\\mathcal C_E=\\{x\\in\\mathcal K(\\mathcal H): \\{s_n(x)\\}\\in E\\}$ with $\\|x\\|_{\\mathcal C_E}=\\|\\{s_n(x)\\}\\|_E$, $x\\in\\mathcal C_E$, be the Banach ideal of compact operators generated by $E$. We show that the averages $A_n(T)(x)=\\frac1{n+1}\\sum\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00759","kind":"arxiv","version":2},"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"}