Small operator ideals formed by s numbers on generalized Cesáro and Orlicz sequence spaces

Abstract

In this article, we establish sufficient conditions on the generalized Cesáro and Orlicz sequence spaces E such that the class SE of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers belonging to E generates an operator ideal. The components of SE as a pre-quasi Banach operator ideal containing finite dimensional operators as a dense subset and its completeness are proved. Some inclusion relations between the operator ideals as well as the inclusion relations for their duals are obtained. Finally, we show that the operator ideal formed by E and approximation numbers is small under certain conditions.