{"paper":{"title":"Isometric dilations and $H^\\infty$ calculus for bounded analytic semigroups and Ritt operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C\\'edric Arhancet, Christian Le Merdy, Stephan Fackler","submitted_at":"2015-04-02T08:21:43Z","abstract_excerpt":"We show that any bounded analytic semigroup on $L^p$ (with $1<p<\\infty$) whose negative generator admits a bounded $H^{\\infty}$ functional calculus with respect to some angle $< \\pi/2$ can be dilated into a bounded analytic semigroup $(R_t)_{t\\geq 0}$ on a bigger $L^p$-space in such a way that $R_t$ is a positive contraction for any $t$. We also establish a discrete analogue for Ritt operators and consider the case when $L^p$-spaces are replaced by more general Banach spaces. In connection with these functional calculus issues, we study isometric dilations of bounded continuous representations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00471","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"}