A note on Nakano generalized difference sequence space
Bakery, Awad A.; Elmatty, Afaf R.Abou;
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.
Other data
Title | A note on Nakano generalized difference sequence space | Authors | Bakery, Awad A. ; Elmatty, Afaf R.Abou | Keywords | Approximable operator;Fredholm operator;Generalized difference;Multiplication operator;Premodular;Simple Banach space | Issue Date | 1-Dec-2020 | Journal | Advances in Difference Equations | ISSN | 16871839 | DOI | 10.1186/s13662-020-03082-1 | Scopus ID | 2-s2.0-85094971044 |
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