{"paper":{"title":"A Bohl-Bohr-Kadets type theorem characterizing Banach spaces not containing c0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B\\'alint Farkas","submitted_at":"2013-01-26T13:16:29Z","abstract_excerpt":"We prove that a separable Banach space $E$ does not contain a copy of the space $\\co$ of null-sequences if and only if for every doubly power-bounded operator $T$ on $E$ and for every vector $x\\in E$ the relative compactness of the sets $\\{T^{n+m}x-T^nx: n\\in \\NN\\}$ (for some/all $m\\in\\NN$, $m\\geq 1$) and $\\{T^nx:n\\in \\NN\\}$ are equivalent. With the help of the Jacobs--de Leeuw--Glicksberg decomposition of strongly compact semigroups the case of (not necessarily invertible) power-bounded operators is also handled."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6250","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"}