{"paper":{"title":"On the Baker-Campbell-Hausdorff Theorem: non-convergence and prolongation issues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-ph","hep-th","math.MP","math.RA"],"primary_cat":"math-ph","authors_text":"Andrea Bonfiglioli, Marco Matone, Stefano Biagi","submitted_at":"2018-05-25T11:45:42Z","abstract_excerpt":"We investigate some topics related to the celebrated Baker-Campbell-Hausdorff Theorem: a non-convergence result and prolongation issues. Given a Banach algebra $\\mathcal{A}$ with identity $I$, and given $X,Y\\in \\mathcal{A}$, we study the relationship of different issues: the convergence of the BCH series $\\sum_n Z_n(X,Y)$, the existence of a logarithm of $e^Xe^Y$, and the convergence of the Mercator-type series $\\sum_n {(-1)^{n+1}}(e^Xe^Y-I)^n/n$ which provides a selected logarithm of $e^Xe^Y$. We fix general results and, by suitable matrix counterexamples, we show that various pathologies can"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10089","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"}