Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces

الملخص EN

In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces cesφ, where φ is an Orlicz function such that the class Scesφ of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers which belong to cesφ forms an operator ideal.

The completeness and denseness of its ideal components are specified and Scesφ constructs a pre-quasi Banach operator ideal.

Some inclusion relations between the pre-quasi operator ideals and the inclusion relations for their duals are explained.

Moreover, we have presented the sufficient conditions on cesφ such that the pre-quasi Banach operator ideal generated by approximation number is small.

The above results coincide with that known for cesp (1