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

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

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