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Then the function $\\phi$ defined by $\\phi(t) = r(t K + (1-t) K^*)$ is non-decreasing on $[0, {1/2}]$. We also prove that $\\| A + B^* \\| \\ge 2 \\cdot \\sqrt{r(A B)}$ for any positive operators $A$ and $B$ on $L^2(X,\\mu)$."},"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":"math/0304253","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2003-04-18T13:00:22Z","cross_cats_sorted":[],"title_canon_sha256":"fe76fda7d70c64112091755770cbf9c8bfea8b48997d102647e0a600571e8590","abstract_canon_sha256":"8955a089cb37c74785cbb73653b8aa579219f570d3e1493c03537343452003c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:31.099061Z","signature_b64":"zAOPXIjHEMc298SBFKy0vop4fUYCuwPqtJqlKiJJIl6/QKo7NrW1EecrKVfU3sw/NkFixsmdti/rhNlf1YVFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d3b30dbd345d1a6be435556e98ed449ad51c0f049a618c800f392359a964920","last_reissued_at":"2026-05-18T03:41:31.098284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:31.098284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A generalization of Levinger's theorem to positive kernel operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Roman Drnov\\v{s}ek","submitted_at":"2003-04-18T13:00:22Z","abstract_excerpt":"We prove some inequalities for the spectral radius of positive operators on Banach function spaces. In particular, we show the following extension of Levinger's theorem. Let $K$ be a positive compact kernel operator on $L^2(X,\\mu)$ with the spectral radius $r(K)$. Then the function $\\phi$ defined by $\\phi(t) = r(t K + (1-t) K^*)$ is non-decreasing on $[0, {1/2}]$. 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