{"paper":{"title":"Clark theory in the Drury-Arveson space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael T. Jury","submitted_at":"2013-08-27T14:53:47Z","abstract_excerpt":"We extend the basic elements of Clark's theory of rank-one perturbations of backward shifts, to row-contractive operators associated to de Branges-Rovnyak type spaces $\\mathcal H(b)$ contractively contained in the Drury-Arveson space on the unit ball in $\\mathbb C^d$. The Aleksandrov-Clark measures on the circle are replaced by a family of states on a certain noncommutative operator system, and the backward shift is replaced by a canonical solution to the Gleason problem in $\\mathcal H(b)$. In addition we introduce the notion of a \"quasi-extreme\" multiplier of the Drury-Arveson space and use i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5887","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"}