{"paper":{"title":"Bounds on the spectral radius of real-valued non-negative Kernels on measurable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Heinz Koeppl, Mark Sinzger, Wasiur R. KhudaBukhsh","submitted_at":"2018-08-01T10:49:16Z","abstract_excerpt":"In this short technical note, we extend a recently published result [Liao2017] on the Perron root (or the spectral radius) of non-negative matrices to real-valued non-negative kernels on an arbitrary measurable space $(\\mathrm{E}, \\mathcal{E})$. To be precise, for any real-valued non-negative kernel $K : \\mathrm{E}\\times \\mathcal{E} \\rightarrow \\mathbb{R}$, we prove that the spectral radius $\\rho(K)$ of $K$ satisfies $$\n  \\inf_{x \\in \\mathrm{E} } \\frac{ \\mathcal{R} K \\cdotp L (x) }{ \\mathcal{R} L (x) } \\le \\rho(K) \\le \\sup_{x \\in \\mathrm{E} } \\frac{ \\mathcal{R} K\\cdotp L (x) }{ \\mathcal{R} L ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00258","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}