Vector valued Orlicz-Lorentz sequence spaces and their operator ideals


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.


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.