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We prove that for the generalized spectral radius $\\rho$ and the joint spectral radius $\\hat{\\rho}$ the inequalities $$\\rho \\left(\\Psi _1 ^{\\left( \\frac{1}{m} \\right)} \\circ \\cdots \\circ \\Psi _m ^{\\left( \\frac{1}{m} \\right)} \\right) \\le \\rho (\\Psi _1 \\Psi _2 \\cdots \\Psi _m) ^{\\frac{1}{m}},$$ $$\\hat{\\rho} \\left(\\Psi _1 ^{\\left( \\frac{1}{m} \\right)} \\circ \\cdots \\circ \\Psi _m ^{\\left( \\frac{1}{m} \\right)} \\right) \\le \\hat{\\rho} (\\Psi _1 \\Psi _2 \\cdots \\Psi _m) ^{\\frac{1}{m}}$$ hold, where $"},"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":"1612.01765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-12-06T11:38:20Z","cross_cats_sorted":[],"title_canon_sha256":"9643d54552750421ef13cc6a7b29036141ed413fc348f5e28c3fa2b729031d57","abstract_canon_sha256":"bd586dce5563a219a2a6522e9f4783641470f4112fd2528665a692c03cc8e178"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:23.977562Z","signature_b64":"sTwpW9KAZC6Iz/2LS6T5Bcbkx1AOghbUL9BuvskPVpp0TuQl1jndXj6PPBs2xnugJd1931vwFGD+eVFNmlSLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98573aa7256379337d6463b2a25c3961f9f23d7245ae7a99d8e9562be7e6a036","last_reissued_at":"2026-05-18T00:53:23.977140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:23.977140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on the joint and generalized spectral radius of Hadamard geometric mean of bounded sets of positive kernel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Aljo\\v{s}a Peperko","submitted_at":"2016-12-06T11:38:20Z","abstract_excerpt":"Let $\\Psi _1, \\ldots \\Psi _m$ be bounded sets of positive kernel operators on a Banach function space $L$. 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