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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.1736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-07T12:58:18Z","cross_cats_sorted":[],"title_canon_sha256":"4d655fa91ffbe3776152b9481c52ed04afcff3e6b8a7df82eeacd64d9146339c","abstract_canon_sha256":"7c3d138916ff4ba16534a1a06a78320a68bc4188287cb694b68ef6675887a5b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:14.768920Z","signature_b64":"ViRbzLmyUt9edzg90Eq9XUIRFF133n8V1ylq+VGOU1mvN9Gl/jtEtsz8peT++sigs9fYdOESEDUyavbLA0X+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d32f8b65a66aaf1cf267f7394cdf297bb3ed319e836af40e0e32b105076d8d8","last_reissued_at":"2026-05-18T03:34:14.768069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:14.768069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.1736","created_at":"2026-05-18T03:34:14.768208+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.1736v1","created_at":"2026-05-18T03:34:14.768208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1736","created_at":"2026-05-18T03:34:14.768208+00:00"},{"alias_kind":"pith_short_12","alias_value":"TUZPRNS2M2VP","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TUZPRNS2M2VPDTZG","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TUZPRNS2","created_at":"2026-05-18T12:28:02.375192+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6","json":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6.json","graph_json":"https://pith.science/api/pith-number/TUZPRNS2M2VPDTZGP5ZZJTPSS6/graph.json","events_json":"https://pith.science/api/pith-number/TUZPRNS2M2VPDTZGP5ZZJTPSS6/events.json","paper":"https://pith.science/paper/TUZPRNS2"},"agent_actions":{"view_html":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6","download_json":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6.json","view_paper":"https://pith.science/paper/TUZPRNS2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.1736&json=true","fetch_graph":"https://pith.science/api/pith-number/TUZPRNS2M2VPDTZGP5ZZJTPSS6/graph.json","fetch_events":"https://pith.science/api/pith-number/TUZPRNS2M2VPDTZGP5ZZJTPSS6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6/action/storage_attestation","attest_author":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6/action/author_attestation","sign_citation":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6/action/citation_signature","submit_replication":"https://pith.science/pith/TUZPRNS2M2VPDTZGP5ZZJTPSS6/action/replication_record"}},"created_at":"2026-05-18T03:34:14.768208+00:00","updated_at":"2026-05-18T03:34:14.768208+00:00"}