M. Poplawski

activity

20162019

collaborators

5 papers

math.FA2019

Ideal boundedness of subseries and rearrangements in Banach spaces vs Banach spaces possessing a copy of $c_{0}$

Michał Popławski

Suppose that $X$ is a Banach space. We will show that $X$ does not contain a copy of $c_{0}$ if and only if for each series which is not unconditionally convergent in $X$ respective…

math.FA2018

Ideal convergent subseries in Banach spaces

Marek Balcerzak, Michał Popławski, Artur Wachowicz

Assume that $I$ is an ideal on $N$ , and $\sum_{n} x_{n}$ is a divergent series in a Banach space $X$ . We study the Baire category, and the measure of the set $A(\mat…

math.GN2018

The Baire category of the hyperspace of nontrivial convergent sequences

Michał Popławski

Assume that $X$ is a regular space. We study topological properties of the family $S_{c} (X)$ of nontrivial convergent sequences in $X$ equipped with the Vietoris topology. We show th…

math.FA2017

Properties of simple density ideals

Adam Kwela, Michał Popławski, Jarosław Swaczyna +1

Let $G$ consist of all functions $g : ω \to [0, \infty)$ with $g (n) \to \infty$ and $\frac{n}{g ( n )} ↛ 0$ . Then for each $g \in G$ the family $\mathcal{Z}_g=\{A\subsete…

math.CA2016

Ideal convergent subsequences and rearrangements for divergent sequences of functions