{"paper":{"title":"The normalized orbit of a bounded normal operator can be a frame","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G\\\"otz E. Pfander, Ilya A. Krishtal","submitted_at":"2026-06-18T18:32:51Z","abstract_excerpt":"Conjecture 3 in [A. Aldroubi, C. Cabrelli, I. Krishtal, and U. Molter, Dynamical Sampling: A Survey, La Matematica 5 (2026), Article 37] postulates that for any bounded normal operator $T$ on a Hilbert space $H$ and any vector $g\\in H$ the system \\[\n  \\left\\{\\frac{T^k g}{\\|T^k g\\|}: k=0,1,2,\\ldots\\right\\} \\] is not a frame. It was motivated by [A. Aldroubi, C. Cabrelli, A. F. \\c{C}akmak, U. Molter, and A. Petrosyan, Iterative actions of normal operators, J. Funct. Anal. 272 (2017), no. 3, 1121--1146], where it was established that such frames do not exist when $T$ is a self adjoint operator. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20848","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/2606.20848/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"}