{"paper":{"title":"Banach spaces with the Daugavet property","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dirk Werner, Gleb Sirotkin, Roman Shvidkoy, Vladimir Kadets","submitted_at":"1997-09-17T00:00:00Z","abstract_excerpt":"A Banach space $X$ is said to have the Daugavet property if every operator $T: X\\to X$ of rank~$1$ satisfies $\\|Id+T\\| = 1+\\|T\\|$. We show that then every weakly compact operator satisfies this equation as well and that $X$ contains a copy of $\\ell_{1}$. However, $X$ need not contain a copy of $L_{1}$. We also study pairs of spaces $X\\subset Y$ and operators $T: X\\to Y$ satisfying $\\|J+T\\|=1+\\|T\\|$, where $J: X\\to Y$ is the natural embedding. This leads to the result that a Banach space with the Daugavet property does not embed into a space with an unconditional basis. In another direction, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9709216","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"}