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On Sequences with at Most a Finite Number of Zero Coordinates
- Publication Year :
- 2024
-
Abstract
- 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-Sep\'ulveda, our research reveals new insights and complements their notable results beyond the classical \( \ell_p \) 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 \( F \setminus Z(F) \), where \( F \) is a closed subspace of \( \ell_p \) containing \( c_0 \), is (alpha, c)-spaceable if and only if alpha is finite.
- Subjects :
- Mathematics - Functional Analysis
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.06859
- Document Type :
- Working Paper