{"paper":{"title":"Composition operators with surjective symbol and small approximation numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Li (LML), Herv\\'e Queff\\'elec (LPP), Luis Rodr\\'iguez-Piazza","submitted_at":"2018-11-13T09:17:32Z","abstract_excerpt":"We give a new proof of the existence of a surjective symbol whose associated composition operator on H 2 (D) is in all Schatten classes, with the improvement that its approximation numbers can be, in some sense, arbitrarily small. We show, as an application, that, contrary to the 1-dimensional case, for N $\\ge$ 2, the behavior of the approximation numbers a n = a n (C $\\Phi$), or rather of $\\beta$ -- N = lim inf n$\\rightarrow$$\\infty$ [a n ] 1/n 1/N or $\\beta$ + N = lim sup n$\\rightarrow$$\\infty$ [a n ] 1/n 1/N , of composition operators on H 2 (D N) cannot be determined by the image of the sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05174","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"}