{"paper":{"title":"Joint spreading models and uniform approximation of bounded operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Georgiou, A.-R. Lagos, P. Motakis, S. A. Argyros","submitted_at":"2017-12-20T18:48:14Z","abstract_excerpt":"We investigate the following property for Banach spaces. A Banach space $X$ satisfies the Uniform Approximation on Large Subspaces (UALS) if there exists $C>0$ with the following property: for any $A\\in\\mathcal{L}(X)$ and convex compact subset $W$ of $\\mathcal{L}(X)$ for which there exists $\\varepsilon>0$ such that for every $x\\in X$ there exists $B\\in W$ with $\\|A(x)-B(x)\\|\\le\\varepsilon\\|x\\|$, there exists a subspace $Y$ of $X$ of finite codimension and a $B\\in W$ with $\\|(A-B)|_Y\\|_{\\mathcal{L}(Y,X)}\\leq C\\varepsilon$. We prove that a class of separable Banach spaces including $\\ell_p$, for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07638","kind":"arxiv","version":3},"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"}