{"paper":{"title":"Almost everywhere convergence of entangled ergodic averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"D\\'avid Kunszenti-Kov\\'acs","submitted_at":"2015-11-04T22:00:37Z","abstract_excerpt":"We study pointwise convergence of entangled averages of the form \\[ \\frac{1}{N^k}\\sum_{1\\leq n_1,\\ldots, n_k\\leq N} T_m^{n_{\\alpha(m)}}A_{m-1}T^{n_{\\alpha(m-1)}}_{m-1}\\ldots A_2T_2^{n_{\\alpha(2)}}A_1T_1^{n_{\\alpha(1)}} f, \\] where $f\\in L^2(X,\\mu)$, $\\alpha:\\left\\{1,\\ldots,m\\right\\}\\to\\left\\{1,\\ldots,k\\right\\}$, and the $T_i$ are ergodic measure preserving transformations on the standard probability space $(X,\\mu)$. We show that under some joint boundedness and twisted compactness conditions on the pairs $(A_i,T_i)$, almost everywhere convergence holds for all $f\\in L^2$. We also present resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01528","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"}