{"paper":{"title":"Local and global liftings of analytic families of idempotents in Banach algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bernard Aupetit, Endre Makai, Jaroslav Zem\\'anek, Jr., Mostafa Mbekhta","submitted_at":"2014-11-18T09:58:10Z","abstract_excerpt":"Generalizing results of our earlier paper, we investigate the following question. Let $\\pi(\\lambda) : A \\to B$ be an analytic family of surjective homomorphisms between two Banach algebras, and $q(\\lambda)$ an analytic family of idempotents in $B$. We want to find an analytic family $p(\\lambda)$ of idempotents in $A$, lifting $q(\\lambda)$, i.e., such that $\\pi(\\lambda)p(\\lambda) = q(\\lambda)$, under hypotheses of the type that the elements of $\\text{Ker}\\, \\pi(\\lambda)$ have small spectra. For spectra which do not disconnect $\\Bbb C$ we obtain a local lifting theorem. For real analytic familie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4788","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"}