{"paper":{"title":"Hypercyclic subspaces on Fr\\'echet spaces without continuous norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Quentin Menet","submitted_at":"2013-02-26T14:49:31Z","abstract_excerpt":"Known results about hypercyclic subspaces concern either Fr\\'echet spaces with a continuous norm or the space \\omega. We fill the gap between these spaces by investigating Fr\\'echet spaces without continuous norm. To this end, we divide hypercyclic subspaces into two types: the hypercyclic subspaces M for which there exists a continuous seminorm p such that M\\cap \\ker p=\\{0\\} and the others. For each of these types of hypercyclic subspaces, we establish some criteria. This investigation permits us to generalize several results about hypercyclic subspaces on Fr\\'echet spaces with a continuous n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6447","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"}