{"paper":{"title":"Operators with Diskcyclic Vectors Subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adem K{\\i}l{\\i}\\c{c}man, Nareen Bamerni","submitted_at":"2015-01-12T04:22:21Z","abstract_excerpt":"In this paper, we prove that if $T$ is diskcyclic operator then the closed unit disk multiplied by the union of the numerical range of all iterations of $T$ is dense in $\\mathcal H$. Also, if $T$ is diskcyclic operator and $|\\lambda|\\le 1$, then $T-\\lambda I$ has dense range. Moreover, we prove that if $\\alpha >1$, then $\\frac{1}{\\alpha}T$ is hypercyclic in a separable Hilbert space $\\mathcal H$ if and only if $T \\oplus \\alpha I_{\\mathbb{C}}$ is diskcyclic in $\\mathcal H \\oplus \\mathbb{C}$. We show at least in some cases a diskcyclic operator has an invariant, dense linear subspace or an infin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02537","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"}