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We first give a complete characterization of such sequences. We then turn to the study of rigidity sequences (n_k) for weakly mixing dynamical systems on measure spaces, and give various conditions, some of which are closely related to the Jamison condition, for a sequence to be a rigidity sequence. We obtain"},"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":"1101.4553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-24T14:47:21Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f5921477ddeeb783d18baf82f1c8b408263c291f610a71459b6501d5694cdb3e","abstract_canon_sha256":"4eaaabd597359328f4770523e5cf1133c82558c2258001f1e8943d3d3f82a1d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:12.903649Z","signature_b64":"FvvJnoNgOPQEne+Y3hThg1m3Oo0n9XKR34DKepV4OCitlAX+fj6uXBZ7NbU01/8iaTiSV1cy0RT+w4QEx+HjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"830a4d4eff61e6798a490aac67dc1eeb3dea1e9555ef0cc681af1aa0a8ecf62e","last_reissued_at":"2026-05-18T04:20:12.903133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:12.903133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbertian Jamison sequences and rigid dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Sophie Grivaux, Tanja Eisner","submitted_at":"2011-01-24T14:47:21Z","abstract_excerpt":"A strictly increasing sequence (n_k) of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that the supremum over k of the norms ||T^{n_k}|| is finite, the set of eigenvalues of modulus 1 of T is at most countable. We first give a complete characterization of such sequences. We then turn to the study of rigidity sequences (n_k) for weakly mixing dynamical systems on measure spaces, and give various conditions, some of which are closely related to the Jamison condition, for a sequence to be a rigidity sequence. 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