{"paper":{"title":"Representations of ideals in Polish groups and in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barnabas Farkas, Grzegorz Plebanek, Piotr Borodulin-Nadzieja","submitted_at":"2014-02-03T17:34:31Z","abstract_excerpt":"We investigate ideals of the form $\\{A \\subseteq \\omega\\colon \\sum_{n\\in A} x_n$ is unconditionally convergent $\\}$, where $(x_n)_{n\\in\\omega}$ is a sequence in a Polish group or in a Banach space. If an ideal on $\\omega$ can be seen in this form for some sequence in $X$, then we say that it is representable in $X$.\n  After numerous examples we show the following theorems: (1) An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. (2) An ideal is representable in a Banach space iff it is a non-pathological analytic P-ideal.\n  We focus on the family of ideals represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0441","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"}