{"paper":{"title":"Narrow and $\\ell_2$-strictly singular operators from $L_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. Randrianantoanina, G. Schechtman, M. Popov, V. Mykhaylyuk","submitted_at":"2012-11-20T20:39:03Z","abstract_excerpt":"In the first part of the paper we prove that for $2 < p, r < \\infty$ every operator $T: L_p \\to \\ell_r$ is narrow. This completes the list of sequence and function Lebesgue spaces $X$ with the property that every operator $T:L_p \\to X$ is narrow.\n  Next, using similar methods we prove that every $\\ell_2$-strictly singular operator from $L_p$, $1<p<\\infty$, to any Banach space with an unconditional basis, is narrow, which partially answers a question of Plichko and Popov posed in 1990.\n  A theorem of H. P. Rosenthal asserts that if an operator $T$ on $L_1[0,1]$ satisfies the assumption that for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4854","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"}