The Baire category of ideal convergent subseries and rearrangements of a divergent series

Speaker(s)

Marek Balcerzak

Affiliation

Politechnika Łódzka

Date

Oct. 25, 2017, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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Let I be a 1-shift-invariant ideal on N with the Baire property. Assume that a series 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. These results were obtained together with Michał Popławski and Artur Wachowicz, and published in Topology Appl. 231 (2017), 219-230.

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