{"paper":{"title":"Connecting $H^\\infty$-functional calculus and isometric dilations for commuting families of Ritt$_E$ operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christian Le Merdy, M. N. Reshmi","submitted_at":"2026-06-26T16:05:38Z","abstract_excerpt":"Let $(T_1,\\ldots,T_d)$ be a commuting $d$-tuple of Ritt$_E$ operators on some UMD Banach space $X$. We show that $(T_1,\\ldots,T_d)$ admits a bounded $H^\\infty$-functional calculus if and only if $T_k$ is an $R$-Ritt$_E$ operator for every $k=1,\\ldots,d$, and the $d$-tuple $(T_1,\\ldots,T_d)$ admits an isometric dilation $(U_1,\\ldots,U_d)$ on some UMD Banach space $Y$ such that $(U_1,\\ldots,U_d)$ is polynomially bounded. In the case where $X$ further possesses property $(\\alpha)$, we establish other characterizations of the $H^\\infty$-functional calculus property for $(T_1,\\ldots,T_d)$ in terms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28214","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28214/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}