Abstract
In this paper, we characterize the matrix classes $(\ell _{1},\ell _{p}(\widehat{F}))$ ( $1\leq p<\infty $ ), where $\ell _{p}(\widehat{F})$ is some Fibonacci difference sequence spaces. We also obtain estimates for the norms of the bounded linear operators $L_{A}$ defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.
Highlights
Introduction and preliminariesLet N = {, . . .} and R be the set of all real numbers
We find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness
Proof Since is a BK space with AK it follows from Lemma . that L ∈ B(, p(F)) for ≤ p < ∞ if and only if there exists an infinite matrix A ∈ (, p(F)) such that ( . ) holds
Summary
Since matrix mappings between BK spaces define bounded linear operators between these spaces which are Banach spaces, it is natural to use the above results and the Hausdorff measure of noncompactness to obtain necessary and sufficient conditions for matrix operators between BK spaces with a Schauder basis or AK to be compact operators. This technique has recently been used by several authors in many research papers (see for instance [ – ]). We find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness
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