Abstract
The sequence spaces , have recently been introduced by Sömez (Comput. Math. Appl. 62:641-650, 2011). In this paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces , and by using the Hausdorff measure of noncompactness, we characterize some classes of compact operators on these spaces. MSC:46A45, 40H05, 40C05.
Highlights
By w, we shall denote the space of all real- or complex-valued sequences
The matrix domain μA of an infinite matrix A in a sequence space μ is defined by μA = x = ∈ ω : Ax ∈ μ
By using the Hausdorff measure of noncompactness, we characterize some classes of compact operators on these spaces
Summary
We shall denote the space of all real- or complex-valued sequences. Any vector subspace of w is called a sequence space. We shall write bs, cs for the spaces of all sequences associated with bounded and convergent series. Let μ and γ be two sequence spaces and A = (ank) be an infinite matrix of real or complex numbers ank, where n, k ∈ N.
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