{"paper":{"title":"Non-commutativity of exponential spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.FA","authors_text":"Hubert Klaja, Thomas Ransford","submitted_at":"2015-10-27T22:04:36Z","abstract_excerpt":"In a Banach algebra, the spectrum satisfies $\\sigma(ab)\\setminus\\{0\\} = \\sigma(ba)\\setminus\\{0\\}$ for each pair of elements $a,b$. We show that this is no longer true for the exponential spectrum, thereby solving a problem open since 1992. Our proof depends on the fact that the homotopy group $\\pi_4(GL_2({\\mathbb C}))$ is non-trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08109","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"}