{"paper":{"title":"Extended eigenvalues for Ces\\`aro operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fernando Le\\'on-Saavedra, John Petrovic, Miguel Lacruz, Omid Zabeti","submitted_at":"2014-03-19T15:28:24Z","abstract_excerpt":"A complex scalar $\\lambda$ is said to be an extended eigenvalue of a bounded linear operator $T$ on a complex Banach space if there is a nonzero operator $X$ such that $TX= \\lambda XT.$ Such an operator $X$ is called an extended eigenoperator of $T$ corresponding to the extended eigenvalue $\\lambda.$ The purpose of this paper is to give a description of the extended eigenvalues for the discrete Ces\\`aro operator $C_0,$ the finite continuous Ces\\`aro operator $C_1$ and the infinite continuous Ces\\`aro operator $C_\\infty$ defined on the complex Banach spaces $\\ell^p,$ $L^p[0,1]$ and $L^p[0,\\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4844","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"}