{"paper":{"title":"Square functions for Ritt operators on noncommutative $L^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"C\\'edric Arhancet","submitted_at":"2011-07-18T12:33:08Z","abstract_excerpt":"For any Ritt operator $T$ acting on a noncommutative $L^p$-space, we define the notion of \\textit{completely} bounded functional calculus $H^\\infty(B_\\gamma)$ where $B_\\gamma$ is a Stolz domain. Moreover, we introduce the `column square functions' $\\norm{x}_{T,c,\\alpha}=\\Bnorm{\\Big(\\sum_{k=1}^{+\\infty}k^{2\\alpha-1}|T^{k-1}(I-T)^{\\alpha}(x)|^2\\Big)^{1/2}}_{L^p(M)}$ and the `row square functions' $\\norm{x}_{T,r,\\alpha}=\\Bnorm{\\Big(\\sum_{k=1}^{+\\infty}k^{2\\alpha-1} |\\Big(T^{k-1}(I-T)^{\\alpha}(x)\\Big)^*|^2\\Big)^{1/2}}_{L^p(M)}$ for any $\\alpha>0$ and any $x\\in L^p(M)$. Then, we provide an example "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3415","kind":"arxiv","version":5},"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"}