Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces. (2nd May 2019) - Bakery, Awad A.; Mohammed, Mustafa M.
Abstract : In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spacesc e s φ, whereφ is an Orlicz function such that the classS c e s φ of all bounded linear operators between arbitrary Banach spaces with its sequence ofs - numbers which belong toc e s φ forms an operator ideal. The completeness and denseness of its ideal components are specified andS c e s φ 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 onc e s φ such that the pre-quasi Banach operator ideal generated by approximation number is small. The above results coincide with that known forc e s p ( 1 < p < ∞ ) .