Absolute and Ordinary Köthe-Toeplitz Duals of Some Sets of Sequences and Matrix Transformations
In this paper we investigate linear operators between arbitrary BK spaces and spaces of sequences that are summable or bounded. We give necessary and sufficient conditions for infinite matrices to map into . Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for to be a compact operator.
The main object of this paper is to introduce and study some sequence spaces which arise from the notation of generalized de la Vallée–Poussin means and the concept of a modulus function.
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