{"paper":{"title":"On a generalized uniform zero-two law for positive contractions of non-commutative $L_1$-spaces and its vector-valued extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Dilmurod Bekbaev, Farrukh Mukhamedov, Inomjon Ganiev","submitted_at":"2016-03-25T03:03:18Z","abstract_excerpt":"First, Ornstein and Sucheston proved that for a given positive contraction $T:L_1\\to L_1$ there exists $m\\in N$ such that $\\big\\|T^{m+1}-T^m\\|<2$ then $$ \\lim_{n\\to\\infty}\\|T^{n+1}-T^n\\|=0. $$ Such a result was labeled as \"zero-two\" law. In the present paper, we prove a generalized uniform \"zero-two\" law for multi-parametric family of positive contractions of the non-commutative $L_1$-spaces. Moreover, we also establish a vector-valued analogous of the uniform \"zero-two\" law for positive contractions of $L_1(M,\\Phi)$-- the non-commutative $L_1$-spaces associated with center valued trace."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07812","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"}