{"paper":{"title":"Growth rates and the peripheral spectrum of positive operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jochen Gl\\\"uck","submitted_at":"2015-12-23T14:16:06Z","abstract_excerpt":"Let $T$ be a positive operator on a complex Banach lattice. It is a long open problem whether the peripheral spectrum $\\sigma_{\\operatorname{per}}(T)$ of $T$ is always cyclic. We consider several growth conditions on $T$, involving its eigenvectors or its resolvent, and show that these conditions provide new sufficient criteria for the cyclicity of the peripheral spectrum of $T$. Moreover we give an alternative proof of the recent result that every (WS)-bounded positive operator has cyclic peripheral spectrum. We also consider irreducible operators $T$. If such an operator is Abel bounded, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07483","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"}