{"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 $L$. 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 $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01765","kind":"arxiv","version":1},"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"}