{"paper":{"title":"Compactness and an approximation property related to an operator ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anil Kumar Karn, Deba Prasad Sinha","submitted_at":"2012-07-09T04:48:48Z","abstract_excerpt":"For an operator ideal $\\mathcal A$, we study the composition operator ideals ${\\mathcal A}\\circ{\\mathcal K}$, ${\\mathcal K}\\circ{\\mathcal A}$ and ${\\mathcal K}\\circ{\\mathcal A}\\circ{\\mathcal K}$, where $\\mathcal K$ is the ideal of compact operators. We introduce a notion of an $\\mathcal A$-approximation property on a Banach space and characterise it in terms of the density of finite rank operators in ${\\mathcal A}\\circ{\\mathcal K}$ and ${\\mathcal K}\\circ{\\mathcal A}$.\n  We propose the notions of $\\ell_{\\infty}$-extension and $\\ell_{1}$-lifting properties for an operator ideal $\\mathcal A$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1947","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"}