A study on Copson operator and its associated sequence space

In this research, we investigate two types of Copson matrices, the generalized Copson matrix and the Copson matrix of order n , and their associated sequence spaces generated by these matrices. We also investigate the topological properties, inclusions, and dual spaces of these new Banach spaces as...

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Bibliographic Details
Published in:Journal of inequalities and applications 2020-04, Vol.2020 (1), p.1-18, Article 120
Main Author: Roopaei, Hadi
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Banach spaces
Copson matrix
Difference sequence space
Domains
Hilbert matrix
Inclusions
Mathematics
Mathematics and Statistics
Norm
Operators (mathematics)
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Summary:In this research, we investigate two types of Copson matrices, the generalized Copson matrix and the Copson matrix of order n , and their associated sequence spaces generated by these matrices. We also investigate the topological properties, inclusions, and dual spaces of these new Banach spaces as well as compute the norm of Copson operators on the well-known matrix domains such as Hilbert and difference sequence spaces. Moreover, in a reverse manner, we investigate the norm of well-known operators on the Copson matrix domains generated with Copson matrices. Through this study we introduce several new inequalities, inclusions, and factorizations for well-known operators.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02388-8