Measures of noncompactness in some new lacunary difference sequence spaces

TL;DR

This paper investigates measures of noncompactness in lacunary difference sequence spaces defined via Orlicz functions, providing identities, estimates, and characterizations of compact operators within these spaces.

Contribution

It introduces new identities and estimates for operator norms and measures of noncompactness in lacunary difference sequence spaces based on Orlicz functions, and characterizes compact operators in these spaces.

Findings

Derived identities and estimates for operator norms

Characterized classes of compact operators

Applied Hausdorff measure of noncompactness

Abstract

In this research article, we establish some identities and estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some lacunary difference sequence spaces defined by Orlicz function. Moreover, we apply our results to characterize some classes of compact operators on those spaces by using the Hausdorff measure of noncompactness.