Orlicz Generalized Difference Sequence Space and the Linked Pre-Quasi Operator Ideal

In this article, the necessary conditions on s-type Orlicz generalized difference sequence space to generate an operator ideal have been examined. Therefore, the s-type Orlicz generalized difference sequence space which fails to generate an operator ideal has been shown. We investigate the sufficient conditions on this sequence space to be premodular Banach special space of sequences, and the constructed pre-quasi operator ideal becomes small, simple, closed, Banach space and has eigenvalues identical with its s-numbers.