Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777726 | Topology and its Applications | 2017 | 12 Pages |
Abstract
Let I be a 1-shift-invariant ideal on N with the Baire property. Assume that a series ânxn with terms in a real Banach space X is not unconditionally convergent. We show that the sets of I-convergent subseries and of I-convergent rearrangements of a given series are meager in the respective Polish spaces. A stronger result, dealing with I-bounded partial sums of a series, is obtained if X is finite-dimensional. We apply the main theorem to series of functions with the Baire property, from a Polish space to a separable Banach space over R, under the assumption that the ideal I is analytic or coanalytic.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Marek Balcerzak, MichaÅ PopÅawski, Artur Wachowicz,