Some properties of pre-quasi norm on Orlicz sequence space
Bakery, Awad A.; Elmatty, Afaf R.Abou;
Abstract
In this article, we introduce the concept of pre-quasi norm on E (Orlicz sequence space), which is more general than the usual norm, and give the conditions on E equipped with the pre-quasi norm to be Banach space. We give the necessity and sufficient conditions on E equipped with the pre-quasi norm such that the multiplication operator defined on E is a bounded, approximable, invertible, Fredholm, and closed range operator. The components of pre-quasi operator ideal formed by the sequence of s-numbers and E is strictly contained for different Orlicz functions are determined. Furthermore, we give the sufficient conditions on E equipped with a pre-modular such that the pre-quasi Banach operator ideal constructed by s-numbers and E is simple and its components are closed. Finally the pre-quasi operator ideal formed by the sequence of s-numbers and E is strictly contained in the class of all bounded linear operators, whose sequence of eigenvalues belongs to E.
Other data
Title | Some properties of pre-quasi norm on Orlicz sequence space | Authors | Bakery, Awad A. ; Elmatty, Afaf R.Abou | Keywords | Approximable operator;Fredholm operator;Multiplication operator;Orlicz sequence space;Pre-quasi norm;Simple Banach space | Issue Date | 1-Jan-2020 | Journal | Journal of Inequalities and Applications | ISSN | 10255834 | DOI | 10.1186/s13660-020-02318-8 | Scopus ID | 2-s2.0-85081030033 |
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