Presentation Abstract

Fame 2026 Conference
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Ideal bases in Banach Spaces

PhD Jarosław Swaczyna (Institute of Mathematics, Łódź University of Technology , Poland) ORCID
Session: Abstract methods in Banach spaces Talk
Abstract

Let $\mathcal I$ be an ideal on $\mathbb N$. A sequence $(e_n)$ in a Banach space $X$ is called an $\mathcal I$-Schauder basis if every $x \in X$ has a unique expansion
\[
x=\sum_{n, \mathcal I} a_n e_n
\]
such that the sequence of partial sums converges to $x$ in the sense of $\mathcal I$-convergence. In this talk, I will discuss recent developments concerning ideal Schauder bases, with particular emphasis on examples obtained jointly with Adam Kwela and on phenomena that distinguish them from classical Schauder bases.