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An easy computation shows that $J$ is a $3$-isometry and that the restriction of $J$ to an invariant subspace is also a $3$-isometry. Those $3$-isometries which are the restriction of a Jordan operator to an invariant subspace can be identified, using the theory of completely posit"},"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":"1508.01273","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-06T04:00:17Z","cross_cats_sorted":[],"title_canon_sha256":"490dd3364f9a2b5dea635dbbfea99b5994b95e43a5d1f64e4cf19e2eb9937c27","abstract_canon_sha256":"d30362636f29d5329f807a74185fed585918822be322dd679e7f62e57bf0887e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:43.016357Z","signature_b64":"4ZtBRadnop6/yhgOrRvqMmSB3b1cMswk5ihJ6oUpxuqRIIB6otEowbDzQJwoTTK2uW3orpwsPYZN3xox4s2mCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"144ab4cca7417d9696b9f0c8b88f5b598944b0c03e55d5286f1f943d84c0ba6b","last_reissued_at":"2026-05-18T01:35:43.015691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:43.015691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifting Commuting 3-Isometric Tuples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Benjamin Russo","submitted_at":"2015-08-06T04:00:17Z","abstract_excerpt":"An operator $T$ is called a 3-isometry if there exists operators $B_1(T^*,T)$ and $B_2(T^*,T)$ such that \\[Q(n)=T^{*n}T^n=1+nB_1(T^*,T)+n^2 B_2(T^*,T)\\] for all natural numbers $n$. An operator $J$ is a Jordan operator of order $2$ if $J=U+N$ where $U$ is unitary, $N$ is nilpotent order $2$, and $U$ and $N$ commute. An easy computation shows that $J$ is a $3$-isometry and that the restriction of $J$ to an invariant subspace is also a $3$-isometry. 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