On the extensions of the almost convergence idea and core theorems

Volume 9, Issue 1, pp 112--125 http://dx.doi.org/10.22436/jnsa.009.01.11

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Authors

Zarife Zararsiz - Department of Mathematics, Nevşehir Hacı Bektaş Veli University, 50300, Nevşehir, Turkey.

Abstract

The sequence spaces \(rf\) and \(rf_0\), more general and comprehensive than the almost convergent sequence spaces \(f\) and \(f_0\), were introduced by Zararsız and Şengönül in [Z. Zararsız, M. Şengönül, Doctoral Thesis, Nevşehir, (2015)]. The purpose of the present paper is to study the sequence spaces \(brf\) and \(brf_0\), that is, the sets of all sequences such that their \(B(r; s)\) transforms are in \(rf\) and \(rf_0\) respectively. Furthermore, we determine the \(\beta\)- and \(\gamma\)- duals of brf, we show that there exists a linear isomorphic mapping between the spaces \(rf\) and \(brf\), and between \(rf_0\) and \(brf_0\) respectively, and provide some matrix characterizations of these spaces. Finally, we introduce the \(B_{RB}\)-core of a complex valued sequence and prove some theorems related to this new type of core.

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Keywords

• Almost convergence
• \(\beta\)- and \(\gamma\)-duals
• matrix domain of a sequence space
• isomorphism
• core theorem.

MSC

•  40C05
•  46A45
•  40J05

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