{"paper":{"title":"On the structure of the set of algebraic elements in a Banach algebra and their liftings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"E. Makai, Jr., J. Zem\\'anek","submitted_at":"2018-07-04T13:04:20Z","abstract_excerpt":"We generalize earlier results about connected components of idempotents in Banach algebras, due to B. Sz\\H{o}kefalvi Nagy, Y. Kato, S. Maeda, Z. V. Kovarik, J. Zem\\'anek, J. Esterle. Let $A$ be a unital complex Banach algebra, and $p(\\lambda) = \\prod\\limits_{i = 1}^n (\\lambda - \\lambda_i)$ a polynomial over $\\Bbb C$, with all roots distinct. Let $E_p(A) := \\{a \\in A \\mid p(a) = 0\\}$. Then all connected components of $E_p(A)$ are pathwise connected (locally pathwise connected) via each of the following three types of paths: 1)~similarity via a finite product of exponential functions (via an exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01552","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"}