{"paper":{"title":"Asymptotics of Operator Semigroups via the Semigroup at Infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jochen Gl\\\"uck, Markus Haase","submitted_at":"2018-11-19T19:54:00Z","abstract_excerpt":"We systematize and generalize recent results of Gerlach and Gl\\\"uck on the strong convergence and spectral theory of bounded (positive) operator semigroups $(T_s)_{s\\in S}$ on Banach spaces (lattices). (Here, $S$ can be an arbitrary commutative semigroup, and no topological assumptions neither on $S$ nor on its representation are required.) To this aim, we introduce the \"semigroup at infinity\" and give useful criteria ensuring that the well-known Jacobs--de Leeuw--Glicksberg splitting theory can be applied to it.\n  Next, we confine these abstract results to positive semigroups on Banach lattic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07955","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"}