{"paper":{"title":"$\\mathcal A$-compact mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pablo Turco","submitted_at":"2015-05-29T13:38:05Z","abstract_excerpt":"For a fixed Banach operator ideal $\\mathcal A$, we use the notion of $\\mathcal A$-compact sets of Carl and Stephani to study $\\mathcal A$-compact polynomials and $\\mathcal A$-compact holomorphic mappings. Namely, those mappings $g\\colon X\\rightarrow Y$ such that every $x \\in X$ has a neighborhood $V_x$ such that $g(V_x)$ is relatively $\\mathcal A$-compact. We show that the behavior of $\\mathcal A$-compact polynomials is determined by its behavior in any neighborhood of any point. We transfer some known properties of $\\mathcal A$-compact operators to $\\mathcal A$-compact polynomials. In order t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08037","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"}