{"paper":{"title":"An inequality concerning the growth bound of a discrete evolution family on a complex Banach space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Constantin Buse, Donal O'Regan, Olivia Saierli","submitted_at":"2016-03-31T13:16:52Z","abstract_excerpt":"We prove that the uniform growth bound $\\omega_0(\\mathcal{U})$ of a discrete evolution family $\\mathcal{U}$ of bounded linear operators acting on a complex Banach space $X$ satisfies the inequality $$\\omega_0(\\mathcal{U})c_{\\mathcal{U}}(\\mathcal{X})\\le -1;$$ here $c_{\\mathcal{U}}(\\mathcal{X})$ is the operator norm of a convolution operator which acts on a certain Banach space $\\mathcal{X}$ of $X$-valued sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09579","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"}