{"paper":{"title":"$C^\\infty$ Functions on the Stone-\\v{C}ech Compactification of the Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Larry B. Schweitzer","submitted_at":"2014-10-03T19:47:53Z","abstract_excerpt":"We construct an algebra $A=\\ell^{\\infty \\infty}({\\Bbb Z})$ of smooth functions which is dense in the pointwise multiplication algebra $\\ell^\\infty({\\Bbb Z})$ of sup-norm bounded functions on the integers $\\Bbb Z$. The algebra $A$ properly contains the sum of the algebra $A_c=\\ell_c^\\infty({\\Bbb Z})$ and the ideal ${\\cal S}({\\Bbb Z})$, where $A_c$ is the algebra of finite linear combinations of projections in $\\ell^\\infty({\\Bbb Z})$ and ${\\cal S}({\\Bbb Z})$ is the pointwise multiplication algebra of Schwartz functions. The algebra $A$ is characterized as the set of functions whose \"first deriva"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0953","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"}