Journal of inequalities and applications | |
Some properties of pre-quasi norm on Orlicz sequence space | |
article | |
Awad A. Bakery1  Afaf R. Abou Elmatty2  | |
[1] Department of Mathematics, College of Science and Arts at Khulis, University of Jeddah;Department of Mathematics, Faculty of Science, Ain Shams University | |
关键词: Pre-quasi norm; Orlicz sequence space; Multiplication operator; Fredholm operator; Approximable operator; Simple Banach space; | |
DOI : 10.1186/s13660-020-02318-8 | |
学科分类:电力 | |
来源: SpringerOpen | |
【 摘 要 】
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.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO202106300003470ZK.pdf | 1568KB | download |