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\\sup\\{ |p(z_1, \\dots, z_n)| : \\textstyle \\sum_{i=1}^{n} \\vert z_{i} \\vert^{q} \\leq 1 \\}\\,. \\] For fixed $k$ and $q$, we study the asymptotic growth of the smallest constant $C_{k,q}(n)$ as $n$ (the number of variables/operators) tends t"},"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":"1504.05547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-21T18:52:51Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"f2cbf120a717375f81007849315bcb66cf98edd4f5f9b973405b6b60fd26bfe6","abstract_canon_sha256":"3414e9f4471614af16845eb5e2cfec9a58d899e76820c6655feb56be96d78b56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:48.854690Z","signature_b64":"3N8C664oPojhY8F/r0aJU+jTHSQPqX1VK/bVAwty0gQ2UyoLj5Df+m7qaZebMOR2S4o2L1Sy7TQrMRzwCcYsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42ee16517cdbe66a969690bb399098a711b00af8e977555bb95b4fe36a988c08","last_reissued_at":"2026-05-18T01:37:48.854159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:48.854159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic estimates on the von Neumann inequality for homogeneous polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Daniel Galicer, Pablo Sevilla-Peris, Santiago Muro","submitted_at":"2015-04-21T18:52:51Z","abstract_excerpt":"By the von Neumann inequality for homogeneous polynomials there exists a positive constant $C_{k,q}(n)$ such that for every $k$-homogeneous polynomial $p$ in $n$ variables and every $n$-tuple of commuting operators $(T_1, \\dots, T_n)$ with $\\sum_{i=1}^{n} \\Vert T_{i} \\Vert^{q} \\leq 1$ we have \\[ \\|p(T_1, \\dots, T_n)\\|_{\\mathcal L(\\mathcal H)} \\leq C_{k,q}(n) \\; 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