Some properties of pre-quasi norm on Orlicz sequence space

Journal of inequalities and applications

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