Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers

TL;DR

This paper investigates the compactness of matrix operators on Fibonacci difference sequence spaces using the Hausdorff measure of noncompactness, providing necessary and sufficient conditions for their compactness.

Contribution

It introduces criteria for compactness of matrix operators on Fibonacci-based sequence spaces, extending the understanding of operator theory in these specialized spaces.

Findings

Derived necessary and sufficient conditions for compactness

Applied Hausdorff measure of noncompactness in this context

Extended operator theory to Fibonacci difference sequence spaces

Abstract

In this paper, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for certain matrix operators on the Fibonacci difference sequence spaces l_{p}(F) and l_{infinite}(F) to be compact, where 1<=p<infinite.