Measure of noncompactness of matrix operators on some difference sequence spaces of weighted means

摘要

For a sequence x = (xk), we denote the difference sequence by △x = (xk - xk-1). Let u = (Uk)∞_(k=0) and v = (vk)∞_(k=0) be sequences of real numbers such that uk≠ 0, vk ≠ 0 for all k ∈ N. The difference sequence spaces of weighted means X(u, v, A) are defined as X(u,v,△)= (x=(xk):W(x)∈λ], where λ = c,c_0 and l_∞ and the matrix W = (ω_nk) is defined by {un(yj-uk+1) (k < n), unun; (k = n), 0; (k > n). In this paper, we establish some identities or estimates for the operator norms and the Hausdorffmeasures of noncompactness of certain matrix operators on k(u, v, A). Further, we characterize some classes of compact operators on these spaces by using the Hausdorff measure of noncompactness.