Acta Mathematica Sinica, English Series

, Volume 34, Issue 5, pp 812–826 | Cite as

On Absolute Nörlund Spaces and Matrix Operators

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Abstract

In a more recent paper, the second author has introduced a space |C α | k as the set of all series by absolute summable using Cesàro matrix of order α > −1. In the present paper we extend it to the absolute Nörlund space |N p θ | k taking Nörlund matrix in place of Cesàro matrix, and also examine some topological structures, α-β-γ-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.

Keywords

Sequence spaces absolute Nörlund summability dual spaces matrix transformations bounded linear operator BK spaces 

MR(2010) Subject Classification

40C05 40D25 40F05 46A45 

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Copyright information

© 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 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and ArtsPamukkale UniversityDenizliTurkey

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