Generalized Limits and Ideal Convergence

Speaker(s)

Mustafa Gülfırat

Affiliation

Ankara University

Language of the talk

Polish

Date

April 8, 2026, 4:15 p.m.

Room

room 4050

Information about the event

pdf file with abstract: https://drive.google.com/file/d/1CflTSvnCDY53jqASG0vBuJzeGIwXYYif/view?usp=sharing

Seminar

Topology and Set Theory Seminar

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Let $\mathcal{I}$ be an ideal on $\mathbb{N}$, the set of positive integers.
Consider the Banach space $m$ of all real bounded sequences $x$ with $\|x\| = \sup_{k}|x_k|$. A positive linear functional $L$ on $m$ is called an $S_{\mathcal{I}}$-limit if $L(\chi_K)=0$ for every characteristic sequence $\chi_K$ of sets $K\subseteq\mathbb{N}$ for which $\mathcal{I}$-$\lim \chi_K=0$. In this talk, we investigate generalized limits associated with ideal convergence. In particular, we study sublinear functionals that both generate and
dominate $S_{\mathcal{I}}$-limits.
The talk is based on joint work with Cihan Orhan. 
The related paper is available at: 
https://doiserbia.nb.rs/ft.aspx?id=0354-51802432259O

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