Jacek Marchwicki

activity

20162019

collaborators

6 papers

math.CA2019

Cardinal functions of purely atomic measures

Szymon Głab, Jacek Marchwicki

Let $μ$ be a purely atomic measure. By $f_{μ} : [0, \infty) \to {0, 1, 2, \dots, ω, c}$ we denote its cardinal function $f_{μ} (t) = ∣ {A \subset N : μ (A) = t} ∣$ . We study t…

math.FA2018

Subsums of conditionally convergent series in finite dimensional spaces

Jacek Marchwicki, Vaclav Vlasak

An achievement set of a series is a set of all its subsums. We study the properties of achievement sets of conditionally convergent series in finite dimensional spaces. The purpose…

math.FA2017

Achievement sets and sum ranges with ideal supports

Jacek Marchwicki

We introduce the notion of ideally supported achievement sets for a series of real numbers. We analize their complexity and topological properties. We compare the notion of ideal a…

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 $\sum_{n = 1}^{\infty} x_{n}$ be a conditionally convergent series in a Banach space and let $τ$ be a permutation of natural numbers. We study the set $\operatorname{LIM}(\sum_{n=1}^…