The new class $L_{z,p,E}$ of $s-$ type operators

Abstract

The purpose of this study is to introduce the class of s-type $Z\left(u,v;l_{p}\left( E\right) \right) $ operators, which we denote by $%L_{z,p,E}\left(X,Y\right) $, we prove that this class is an operator ideal and quasi-Banach operator ideal by a quasi-norm defined on this class. Then we define classes using other examples of $ s$-number sequences. We conclude by investigating which of these classes are injective, surjective or symmetric.

Keywords

• block sequence space
• operator ideal
• s-numbers
• quasi-norm