Multiplier Sequence Spaces Defined by Statistical Summability and Orlicz-Pettis Theorem
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.42, no.12, pp.1410-1422, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 42 Issue: 12
- Publication Date: 2021
- Doi Number: 10.1080/01630563.2021.1961803
- Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
- Page Numbers: pp.1410-1422
- Keywords: Statistical convergence, Orlicz-Pettis Theorem, weakly unconditionally Cauchy series, completeness, CONVERGENT SEQUENCES, MATRIX SUMMABILITY, NORMED SPACES, COMPLETENESS, DENSITY, SERIES, MODULI
- Inonu University Affiliated: Yes
Abstract
In this paper, we introduce some new multiplier spaces related to a series Sigma(i)x(i) in a normed space X through f-statistical summability and give some characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in X and X*, respectively. We also obtain a new version of the Orlicz-Pettis theorem within the frame of the f-statistical convergence.