Vector valued Orlicz-Lorentz sequence spaces and their operator ideals

Volume 10, Issue 2, pp 338--353 http://dx.doi.org/10.22436/jnsa.010.02.01

Publication Date: February 20, 2017 Submission Date: August 05, 2016

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Authors

S. A. Mohiuddine - Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. K. Raj - School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, J&K, India.

Abstract

In the present paper we introduce and study vector valued Orlicz-Lorentz sequence spaces \(l_{p,q,M,u,\Delta,A}(X)\) on Banach space \(X\) with the help of a Musilak-Orlicz function \(M\) and for different positive indices p and q. We also study their cross and topological duals. Finally, we introduce the operator ideals with the help of the corresponding scalar sequence spaces and s-numbers.

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Keywords

• Lorentz sequence spaces
• s-numbers of operators
• Musielak-Orlicz function
• difference sequence spaces
• operator ideals.

MSC

•  46A45
•  47B06
•  47L20

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