2024/06/11 by Diego Alves, Geivison Ribeiro, Alves, Diego +1
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2406.06859
openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we analyze the existence of algebraic and topological structures in the set of sequences that contain only a finite number of zero coordinates. Inspired by the work of Daniel Cariello and Juan B. Seoane-Sepúlveda, our research reveals new insights and complements their notable results beyond the classical \( ℓp \) spaces for \( p \) in the interval from 1 to infinity, including the intriguing case where \( p \) is between 0 and 1. Our exploration employs notions such as S-lineability, pointwise lineability, and (alpha, beta)-spaceability. This investigation allowed us to verify, for instance, that the set \( F ∖ Z(F) \), where \( F \) is a closed subspace of \( ℓp \) containing \( c0 \), is (alpha, c)-spaceable if and only if alpha is finite.