{"paper":{"title":"Extension and lifting of operators and polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jes\\'us M.F. Castillo, Jes\\'us Su\\'arez, Ricardo Garc\\'ia","submitted_at":"2011-06-25T01:11:39Z","abstract_excerpt":"We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of $\\mathcal{L}_1$ and $\\mathcal{L}_{\\infty}$-spaces that includes and extends those of Lindenstrauss-Rosenthal \\cite{LR} using compact operators and Gonz\\'{a}lez-Guti\\'{e}rrez \\cite{GG} using compact polynomials. We display several examples to show the difference between extending and lifting compact (resp. weakly compact, unconditionally convergent, separable and Rosenthal) operators "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5088","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"}