{"paper":{"title":"Ideal convergent subseries in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Artur Wachowicz, Marek Balcerzak, Micha{\\l} Pop{\\l}awski","submitted_at":"2018-03-09T21:34:00Z","abstract_excerpt":"Assume that $\\mathcal{I}$ is an ideal on $\\mathbb{N}$, and $\\sum_n x_n$ is a divergent series in a Banach space $X$. We study the Baire category, and the measure of the set $A(\\mathcal{I}):=\\left\\{t \\in \\{0,1\\}^{\\mathbb{N}} \\colon \\sum_n t(n)x_n \\textrm{ is } \\mathcal{I}\\textrm{-convergent}\\right\\}$. In the category case, we assume that $\\mathcal{I}$ has the Baire property and $\\sum_n x_n$ is not unconditionally convergent, and we deduce that $A(\\mathcal{I})$ is meager. We also study the smallness of $A(\\mathcal{I})$ in the measure case when the Haar probability measure $\\lambda$ on $\\{0,1\\}^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03699","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"}