Some new Fibonacci difference spaces of non-absolute type and compact operators

TL;DR

This paper introduces new Fibonacci difference sequence spaces of non-absolute type, explores their duals and bases, and characterizes compact operators acting on these spaces using measures of noncompactness.

Contribution

It defines new Fibonacci difference spaces of non-absolute type, determines their duals and bases, and characterizes classes of compact operators on these spaces.

Findings

Introduced the spaces $c_{0}^{}(\u02c8F)$ and $c^{}()$.

Derived inclusion relations and duals of these spaces.

Characterized classes of compact operators on these spaces.

Abstract

The aim of the paper is to introduced the spaces $c_{0}^{\lambda}(\hat{F})$ and $c^{\lambda}(\hat{F})$ which are the BK-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the $\alpha-,\beta-,\gamma-$duals of those spaces and also construct their bases. We also characterize some matrix classes on the spaces $c_{0}^{\lambda}(\hat{F})$ and $c^{\lambda}(\hat{F}).$ Here we characterize the subclasses $\mathcal{K}(X,Y)$ of compact operators where $X$ is $c_{0}^{\lambda}(\hat{F})$ or $c^{\lambda}(\hat{F})$ and $Y$ is one of the spaces $c_{0},c, l_{\infty}, l_{1}, bv$ by applying Hausdorff measure of noncompactness.