English

A Quest for Convergence: Exploring Series in Non-Linear Environments

Functional Analysis 2024-06-04 v1

Abstract

This note presents an extension of a result within the concept of [S]-lineability, originally developed in 2019 by L. Bernal-Gonz\'alez, J.A. Conejero, M. Murillo-Arcila, and J.B. Seoane-Sep\'ulveda . Additionally, we provide a characterization in terms of lineability in the context of complements of unions of closed subspaces in F-spaces, and finally, we present a negative result in both normed spaces and p-Banach spaces. These findings contribute to the understanding of linearity in exotic settings in topological vector spaces.

Keywords

Cite

@article{arxiv.2406.00269,
  title  = {A Quest for Convergence: Exploring Series in Non-Linear Environments},
  author = {Geivison Ribeiro},
  journal= {arXiv preprint arXiv:2406.00269},
  year   = {2024}
}
R2 v1 2026-06-28T16:49:18.355Z