{"paper":{"title":"Geometric aspects of the Daugavet property","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"R. Shvidkoy","submitted_at":"1999-03-16T22:00:53Z","abstract_excerpt":"Let X be a closed subspace of a Banach space Y and J be the inclusion map. We say that the pair (X,Y) has the Daugavet property if for every rank one bounded linear operator T from X to Y the following equality \\|J+T\\|=1+\\|T\\| holds. A new characterization of the Daugavet property in terms of weak open sets is given. It is shown that the operators not fixing copies of l_1 on a Daugavet pair satisfy the Daugavet equation.\n Some hereditary properties are found: if X is a Daugavet space and Y is its subspace, then Y is also a Daugavet space provided X/Y has the Radon-Nikodym property; if Y is ref"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9903098","kind":"arxiv","version":2},"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"}