{"paper":{"title":"Approximation sequences on Banach spaces: a rich approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.OA"],"primary_cat":"math.FA","authors_text":"Helena Mascarenhas, Markus Seidel, Pedro A. Santos","submitted_at":"2016-03-20T12:29:10Z","abstract_excerpt":"Criteria for the stability of finite sections of a large class of convolution type operators on $L^p(\\mathbb{R})$ are obtained. In this class almost all classical symbols are permitted, namely operators of multiplication with functions in $[\\textrm{PC} ,\\textrm{SO}, L^\\infty_0]$ and convolution operators (as well as Wiener-Hopf and Hankel operators) with symbols in $[\\textrm{PC},\\textrm{SO},\\textrm{AP},\\textrm{BUC}]_p$. We use a simpler and more powerful algebraic technique than all previous works: the application of $\\mathcal{P}$-theory together with the rich sequences concept and localizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06210","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"}