{"paper":{"title":"A characterization of Banach spaces containing $c_0$","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haskell P. Rosenthal","submitted_at":"1992-10-08T15:45:24Z","abstract_excerpt":"A subsequence principle is obtained, characterizing Banach spaces containing $c_0$, in the spirit of the author's 1974 characterization of Banach spaces containing $\\ell^1$.\n  Definition: A sequence $(b_j)$ in a Banach space is called {\\it strongly summing\\/} (s.s.) if $(b_j)$ is a weak-Cauchy basic sequence so that whenever scalars $(c_j)$ satisfy $\\sup_n \\|\\sum_{j=1}^n c_j b_j\\| <\\infty$, then $\\sum c_j$ converges.\n  A simple permanence property: if $(b_j)$ is an (s.s.) basis for a Banach space $B$ and $(b_j^*)$ are its biorthogonal functionals in $B^*$, then $(\\sum_{j=1}^n b_j^*)_{n=1}^ \\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9210205","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"}