{"paper":{"title":"Extension of hypercyclic and frequently hypercyclic subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Felipe Carvalho Silva, Geivison Ribeiro, R\\'egis Var\\~ao","submitted_at":"2026-04-18T23:04:36Z","abstract_excerpt":"We focus on the existence of large linear structures within the sets of hypercyclic and frequently hypercyclic vectors. For operators $T$ satisfying Kitai's Criterion or the Frequent Hypercyclicity Criterion, we analyze the fundamental linear space $\\{f(T)x | f \\in H(\\mathbb{C})\\}$, studied by Herrero, Bourdon, B\\`es, Wengenroth, and many others. We show that the set $\\{f(T)x | f \\in H(\\mathbb{C})\\}$ can be extended within $HC(T) \\cup \\{0\\}$ or $FHC(T) \\cup \\{0\\}$ if $x \\in HC(T)$ or $x \\in FHC(T)$, respectively. The extension is such that the quotient of the new space with $\\{ f(T)x \\mid f \\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18252","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/2606.18252/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"}