Study of the range of sums of a vector series by multiplying the rearrangements of a series by real numbers (Q1876429)

The author considers a new notion connected with the problem of the range of sums of a series in an infinite-dimensional space, multiplication of a rearrangement of a series by a real number. She distinguishes some sets of rearrangements that admit multiplication by integers. If the sum of a series changes after applying one of these rearrangements then the range of sums is unbounded and one can indicate some elements in it. For some subsets of rearrangements in this set, the author proves the impossibility of multiplying a rearrangement by nonintegral numbers. This is an English translation of the author's article [Mat. Tr. 4, 36--67 (2001; Zbl 0986.46005)].