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arXiv · 1706.07289

Some Fibonacci sequence spaces of non-absolute type derived from $\ell_{p} $ with $(1 \leq p \leq \infty)$ and Hausdorff measure of non-compactness of composition operators

Anupam Das·Bipan Hazarika·Feyzi Başar
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Abstract

The aim of the paper is to introduce the spaces $\ell_{\infty}^λ(\widehat{F})$ and $\ell_{p}^λ(\widehat{F})$ derived by the composition of the two infinite matrices $Λ=(λ_{nk})$ and $\widehat{F}=\left( f_{nk} \right),$ 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 the basis for $\ell_{p}^λ(\widehat{F}).$ Additionally, we characterize some matrix classes on the spaces $\ell_{\infty}^λ(\widehat{F})$ and $\ell_{p}^λ(\widehat{F}).$ We also investigate some geometric properties concerning Banach-Saks type $p.$ Here we characterize the subclasses $\mathcal{K}(X:Y)$ of compact operators, where $X\in\{\ell_{\infty}^λ(\widehat{F}),\ell_{p}^λ(\widehat{F})\}$ and $Y\in\{c_{0},c, \ell_{\infty}, \ell_{1}, bv\}$ by applying the Hausdorff measure of non-compactness, and $1\leq p<\infty.$

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Anupam Das, Bipan Hazarika, Feyzi Başar. 2017-06-18. Some Fibonacci sequence spaces of non-absolute type derived from $\ell_{p} $ with $(1 \leq p \leq \infty)$ and Hausdorff measure of non-compactness of composition operators. https://arxiv.org/abs/1706.07289

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