Advances in Difference Equations | |
A note on Nakano generalized difference sequence space | |
Awad A. Bakery1  Afaf R. Abou Elmatty2  | |
[1] Department of Mathematics, College of Science and Arts at Khulis, University of Jeddah, Jeddah, Saudi Arabia;Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt;Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt; | |
关键词: Premodular; Generalized difference; Simple Banach space; Multiplication operator; Approximable operator; Fredholm operator; | |
DOI : 10.1186/s13662-020-03082-1 | |
来源: Springer | |
【 摘 要 】
In this paper, we investigate the necessary conditions on any s-type sequence space to form an operator ideal. As a result, we show that the s-type Nakano generalized difference sequence space X fails to generate an operator ideal. We investigate the sufficient conditions on X to be premodular Banach special space of sequences and the constructed prequasi-operator ideal becomes a small, simple, and closed Banach space and has eigenvalues identical with its s-numbers. Finally, we introduce necessary and sufficient conditions on X explaining some topological and geometrical structures of the multiplication operator defined on X.
【 授权许可】
CC BY
【 预 览 】
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