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If weak density is replaced by weak sequential density, then $T$ is said to be weakly sequentially hypercyclic or supercyclic respectively. It is shown that on a separable Hilbert space there are weakly supercyclic operators which are not weakly sequentially s"},"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":"1209.1462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:41:00Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0d2691ca0bfa0abfe980ee3f55038a06448723325122ee0fc2073c6696b187db","abstract_canon_sha256":"e683fee3645738142dd55d7d989233a6990b4bdfd395f433a2af827081b46a36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:04.700446Z","signature_b64":"xHZqXrBSe9qNzVecz9QMzucsjTgTobq6xiI0gx5gBGJJdlRDMm77gQyKopm41GOxBQTEVTJW90HYnCyyb/HLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"524f2dafc9b9a943be6454e5c8cdb450219ef0cfb1150b73e462659ae9edd756","last_reissued_at":"2026-05-18T03:46:04.699107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:04.699107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-sequential weak supercyclicity and hypercyclicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2012-09-07T08:41:00Z","abstract_excerpt":"A bounded linear operator $T$ acting on a Banach space $\\B$ is called weakly hypercyclic if there exists $x\\in \\B$ such that the orbit ${T^n x: n=0,1,...}$ is weakly dense in $\\B$ and $T$ is called weakly supercyclic if there is $x\\in \\B$ for which the projective orbit ${\\lambda T^n x: \\lambda \\in \\C, n=0,1,...}$ is weakly dense in $\\B$. If weak density is replaced by weak sequential density, then $T$ is said to be weakly sequentially hypercyclic or supercyclic respectively. 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