3 papers
math.FA2017
Levy-Steinitz theorem and achievement sets of conditionally convergent series on the real plane
Szymon Glab, Jacek Marchwicki
Levy-Steinitz theorem characterize sum range of conditionally convergent series, that is a set of all its convergent rearrangements; in finitely dimensional spaces -- it is an affi…
math.FA2016
Achievement sets of conditionally convergent series
Artur Bartoszewicz, Szymon Głab, Jacek Marchwicki
Considering the sets of subsums of series (or achievement sets) we show that for conditionally convergent series the multidimensional case is much more complicated than that of the…
math.FA2016
On the set of limit points of conditionally convergent series
Szymon Głab, Jacek Marchwicki
Let be a conditionally convergent series in a Banach space and let be a permutation of natural numbers. We study the set $\operatorname{LIM}(\sum_{n=1}^…