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 andalso 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 thesubclasses $\mathcal{K}(X,Y)$ of compact operators where $X$ is$c_{0}^{\lambda}(\hat{F})$ or $c^{\lambda}(\hat{F})$ and $Y$ is one of thespaces $c_{0},c, l_{\infty}, l_{1}, bv$ by applying Hausdorff measure ofnoncompactness.
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机译：本文的目的是介绍空间$ c_ {0} ^ {\ lambda}（\ hat {F}）$和$ c ^ {\ lambda}（\ hat {F}）$这两个BK空间。是非绝对类型的，并且还得出一些包含关系。此外，我们确定这些空间的$ \ alpha-，\ beta- \γ-$ duals并构造它们的基数。我们还对$ c_ {0} ^ {\ lambda}（\ hat {F}）$和$ c ^ {\ lambda}（\ hat {F}）。$。这里我们描述了紧凑运算符的子类$ \ mathcal {K}（X，Y）$，其中$ X $是$ c_ {0 } ^ {\ lambda}（\ hat {F}）$或$ c ^ {\ lambda}（\ hat {F}）$$和$ Y $是$ c_ {0}，c，l _ {\ infty }，l_ {1}，bv $，方法是应用Hausdorff非紧致性度量。
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