Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces

and Applied Analysis 3 Lemma 1.4 see 2 . Let X ⊃ φ be a BK-space and Y any of the spaces c0, c, or ∞. If A ∈ X,Y , then ‖LA‖ ‖A‖ X, ∞ sup n ‖An‖X < ∞, 1.4 where ‖A‖ X, ∞ denotes the operator norm for the matrix A ∈ X, ∞ . Sargent 3 defined the following sequence spaces. Let C denote the space whose elements are finite sets of distinct positive integers. Given any element σ of C, we denote by c σ the sequence {cn σ } such that cn σ 1 for n ∈ σ and cn σ 0 otherwise. Further