{"paper":{"title":"A note on the periodic decomposition problem for semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B\\'alint Farkas","submitted_at":"2014-01-06T21:20:26Z","abstract_excerpt":"Given $T_1,\\dots, T_n$ commuting power-bounded operators on a Banach space we study under which conditions the equality $\\ker (T_1-\\mathrm{I})\\cdots (T_n-\\mathrm{I})=\\ker(T_1-\\mathrm{I})+\\cdots +\\ker (T_n-\\mathrm{I})$ holds true. This problem, known as the periodic decomposition problem, goes back to I. Z. Ruzsa. In this short note we consider the case when $T_j=T(t_j)$, $t_j>0$, $j=1,\\dots, n$ for some one-parameter semigroup $(T(t))_{t\\geq 0}$. We also look at a generalization of the periodic decomposition problem when instead of the cyclic semigroups $\\{T_j^n:n \\in \\mathbb{N}\\}$ more genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1226","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"}