{"paper":{"title":"Clark model in general situation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Constanze Liaw, Sergei Treil","submitted_at":"2013-08-15T03:35:42Z","abstract_excerpt":"For a unitary operator the family of its unitary perturbations by rank one operators with fixed range is parametrized by a complex parameter $\\gamma, |\\gamma|=1$. Namely all such unitary perturbations are $U_\\gamma:=U+(\\gamma-1) (., b_1)_{\\mathcal H} b$, where $b\\in\\mathcal H, \\|b\\|=1, b_1=U^{-1} b, |\\gamma|=1$. For $|\\gamma|<1$ operators $U_\\gamma$ are contractions with one-dimensional defects.\n  Restricting our attention on the non-trivial part of perturbation we assume that $b$ is cyclic for $U$. Then the operator $U_\\gamma$, $|\\gamma|<1$ is a completely non-unitary contraction, and thus un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3298","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"}