Measures of noncompactness in some new lacunary difference sequence spaces
Ekrem Savas, Stuti Borgohain

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.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Advanced Harmonic Analysis Research · Advanced Banach Space Theory
