On Absolute Nörlund Spaces and Matrix Operators

Abstract

In a more recent paper, the second author has introduced a space |C?|k as the set of all series by absolute summable using Cesàro matrix of order ? > -1. In the present paper we extend it to the absolute Nörlund space |Np ?|k taking Nörlund matrix in place of Cesàro matrix, and also examine some topological structures, ?-ß-?-duals and the Schauder base of this space. Further we characterize certain matrix operators on that space and determine their operator norms, and so extend some well-known results. © 2017, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.