{"paper":{"title":"Almost band preservers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pedro Tradacete, Timur Oikhberg","submitted_at":"2016-10-08T16:58:33Z","abstract_excerpt":"We study the stability of band preserving operators on Banach lattices. To this end the notion of $\\varepsilon$-band preserving mapping is introduced. It is shown that, under quite general assumptions, a $\\varepsilon$-band preserving operator is in fact a small perturbation of a band preserving one. However, a counterexample can be produced in some circumstances. Some results on automatic continuity of $\\varepsilon$-band preserving maps are also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02557","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"}