In this paper, we intend to form certain estimates and identities for the norm of matrix operator from \(\ell _{r}\)-type binomial fractional difference sequence space into \(c, c_{0}, \ell _{\infty }\) and \(\ell _{1}\) sequences spaces. We obtain the necessary and sufficient conditions for some classes of compact operators on \(\ell _{r}\)-type binomial fractional difference sequence space \((1 \le r < \infty )\) by employing the Hausdorff measure of non-compactness.

中文翻译：

---

二项式分数差分序列空间上的紧算子

在本文中，我们打算从\（\ ell _ {r} \） -型二项式分数差序列空间到\（c，c_ {0}，\ ell _ { \ infty} \）和\（\ ell _ {1} \）对空格进行排序。我们通过使用Hausdorff测度获得\（\ ell _ {r} \） -型二项式分数差序列空间\（（1 \ le r <\ infty）\）上某些紧致算符的充要条件。非紧凑