This article is cited in 2 papers

On the set of sums of a conditionally convergent series of functions

P. A. Kornilov


Abstract: This article concerns questions connected with the structure of the set of sums of series in a Banach space, i.e., the set of all limit functions for convergent rearrangements of a given series.
It is proved that in any Banach space there exist series for which the set of sums consists of two points, series for which it forms a finite or infinite arithmetic progression, and series for which it is a finite-dimensional lattice.
Stronger results are obtained separately for the spaces $L_p(0, 1)$ with $1\leqslant p<\infty$ and for convergence in measure of series of functions.
Bibliography: 5 titles.

UDC: 517.521

MSC: Primary 40A30, 42C20; Secondary 46E30, 28A20, 46B99

Received: 17.03.1988

 English version: Mathematics of the USSR-Sbornik, 1990, 65:1, 119–131

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