{"paper":{"title":"Vector lattices admitting a positively homogeneous continuous function calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Niels Jakob Laustsen, Vladimir G. Troitsky","submitted_at":"2019-01-22T18:55:34Z","abstract_excerpt":"We characterize the Archimedean vector lattices that admit a positively homogeneous continuous function calculus by showing that the following two conditions are equivalent for each $n$-tuple $\\boldsymbol{x} = (x_1,\\ldots,x_n)\\in X^n$, where $X$ is an Archimedean vector lattice and $n\\in\\mathbb N$:\n  - there is a vector lattice homomorphism $\\Phi_{\\boldsymbol{x}}\\colon H_n\\to X$ such that $\\Phi_{\\boldsymbol{x}}(\\pi_i^{(n)})=x_i$ $(i\\in\\{1,\\ldots,n\\})$, where $H_n$ denotes the vector lattice of positively homogeneous, continuous, real-valued functions defined on $\\mathbb R^n$ and $\\pi_i^{(n)}\\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07522","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"}