{"paper":{"title":"Some properties of subspaces-hypercyclic operators","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 Sabih","submitted_at":"2014-06-04T06:49:37Z","abstract_excerpt":"In this paper, we answer a question posed in the introduction of \\cite{sub hyp} positively, i.e, we show that if $T$ is $\\mathcal M$-hypercyclic operator with $\\mathcal M$-hypercyclic vector $x$ in a Hilbert space $\\mathcal H$, then $P(Orb(T,x))$ is dense in the subspace $\\mathcal M$ where $P$ is the orthogonal projection onto $\\mathcal M$. Furthermore, we give some relations between ${\\mathcal M}^{\\perp}$-hypercyclicity and the orthogonal projection onto ${\\mathcal M}^{\\perp}$. We also give sufficient conditions for a bilateral weighted shift operators on a Hilbert space $\\ell^{2}(\\mathbb Z)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0951","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"}