Abstract

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.

Details

Title
A note on Nakano generalized difference sequence space
Author
Bakery Awad A 1   VIAFID ORCID Logo  ; Elmatty Afaf R Abou 2 

1  University of Jeddah, Department of Mathematics, College of Science and Arts at Khulis, Jeddah, Saudi Arabia (GRID:grid.460099.2); Ain Shams University, Department of Mathematics, Faculty of Science, Abbassia, Egypt (GRID:grid.7269.a) (ISNI:0000 0004 0621 1570) 
2  Ain Shams University, Department of Mathematics, Faculty of Science, Abbassia, Egypt (GRID:grid.7269.a) (ISNI:0000 0004 0621 1570) 
Publication year
2020
Publication date
Dec 2020
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13662-020-03082-1
ProQuest document ID
2471927251
Copyright
© The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.