{"paper":{"title":"Lipschitz spaces and M-ideals","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dirk Werner, Heiko Berninger","submitted_at":"2002-01-16T14:00:18Z","abstract_excerpt":"For a metric space $(K,d)$ the Banach space $\\Lip(K)$ consists of all scalar-valued bounded Lipschitz functions on $K$ with the norm $\\|f\\|_{L}=\\max(\\|f\\|_{\\infty},L(f))$, where $L(f)$ is the Lipschitz constant of $f$. The closed subspace $\\lip(K)$ of $\\Lip(K)$ contains all elements of $\\Lip(K)$ satisfying the $\\lip$-condition $\\lim_{0<d(x,y)\\to 0}|f(x)-f(y)|/d(x,y)=0$. For $K=([0,1],| {\\cdot} |^{\\alpha})$, $0<\\alpha<1$, we prove that $\\lip(K)$ is a proper $M$-ideal in a certain subspace of $\\Lip(K)$ containing a copy of $\\ell^{\\infty}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201144","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"}