{"paper":{"title":"Self-Induced Compactness in Banach Spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hans Jarchow, Peter G. Casazza","submitted_at":"1994-03-28T17:54:36Z","abstract_excerpt":"The question which led to the title of this note is the following:\n  {\\it If $X$ is a Banach space and $K$ is a compact subset of $X$, is it possible to find a compact, or even approximable, operator $v:X\\to X$ such that $K\\subset\\ol{v(B_X)}$?}\n  This question was first posed by P.G.Dixon [6] in connection with investigating the problem of the existence of approximate identities in certain operator algebras. We shall provide a couple of observations related to the above question and give in particular a negative answer in case of approximable operators.\n  We shall also provide the first exampl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9403210","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"}