{"paper":{"title":"Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\\infty}(\\mathbb{N})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Amir Bahman Nasseri, Antonios Manoussos, George Costakis","submitted_at":"2013-02-07T12:58:18Z","abstract_excerpt":"Let $B$, $I$ be the unweighted backward shift and the identity operator respectively on $l^{\\infty}(\\mathbb{N})$, the space of bounded sequences over the complex numbers endowed with the supremum norm. We prove that $I+\\lambda B$ is locally topologically transitive if and only if $|\\lambda |>2$. This, shows that a classical result of Salas, which says that backward shift perturbations of the identity operator are always hypercyclic, or equivalently topologically transitive, on $l^p(\\mathbb{N})$, $1\\leq p<+\\infty$, fails to hold for the notion of local topological transitivity on $l^{\\infty}(\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1736","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"}