A note on Nakano generalized difference sequence space

Advances in Difference Equations

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