{"paper":{"title":"Approximation schemes satisfying Shapiro's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J. M. Almira, T. Oikhberg","submitted_at":"2010-03-17T17:16:57Z","abstract_excerpt":"An approximation scheme is a family of homogeneous subsets $(A_n)$ of a quasi-Banach space $X$, such that $A_1 \\subsetneq A_2 \\subsetneq ... \\subsetneq X$, $A_n + A_n \\subset A_{K(n)}$, and $\\bar{\\cup_n A_n} = X$. Continuing the line of research originating at a classical paper by S.N. Bernstein (in 1938), we give several characterizations of the approximation schemes with the property that, for every sequence $\\{\\epsilon_n\\}\\searrow 0$, there exists $x\\in X$ such that $dist(x,A_n)\\neq \\mathbf{O}(\\epsilon_n)$ (in this case we say that $(X,\\{A_n\\})$ satisfies Shapiro's Theorem). If $X$ is a Ban"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3411","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"}