Erfanmanesh, Saedeh; Foroutannia, D. Generalizations of Köthe-Toeplitz duals and null duals of new difference sequence spaces. (English) Zbl 1367.46005 J. Contemp. Math. Anal., Armen. Acad. Sci. 51, No. 3, 125-133 (2016) and Izv. Nats. Akad. Nauk Armen., Mat. 51, No. 3, 28-40 (2016). Summary: The main purpose of the paper is to generalize the notions of the Köthe-Toeplitz duals and null duals of sequence spaces by introducing the concepts of \(\alpha EF\)-, \(\beta EF\)-, \(\gamma EF\)-duals and \(NEF\)-duals, where \(E = (E_n)\) and \(F = (F_n)\) are two partitions of finite subsets of the positive integers. These duals are computed for the classical sequence spaces \(l_c\) and \(c_0\). The other purpose of the paper is to introduce the sequence spaces \[ X(E,\Delta) = \left\{ x = \left(x_k\right):\left(\sum\limits_{i \in {E_k}} x_i - \sum\limits_{i \in {E_{k - 1}}} {{x_i}}\right)^\infty_{k=1}\in X \right\} \] where \(X \in \left\{l_\infty,c,c_0\right\}\). We investigate the topological properties of these spaces, establish some inclusion relations between them, and compute the \(NEF\)- (or null) duals for these spaces. Cited in 3 Documents MSC: 46A45 Sequence spaces (including Köthe sequence spaces) 40A05 Convergence and divergence of series and sequences 40C05 Matrix methods for summability Keywords:semi-normed sequence space; difference sequence space; matrix domain; \(\alpha\)-dual; \(\beta\)-dual; \(\gamma\)-dual; \(N\)-dual PDFBibTeX XMLCite \textit{S. Erfanmanesh} and \textit{D. Foroutannia}, J. Contemp. Math. Anal., Armen. Acad. Sci. 51, No. 3, 125--133 (2016; Zbl 1367.46005) Full Text: DOI References: [1] F. Başar, Summability Theory and Its Applications (Bentham, Istanbul, 2012). · Zbl 1342.40001 [2] F. Başar, B. Altay and M. Mursaleen, “Some generalizations of the space bvp of p-bounded variation sequences”, Nonlinear Anal., 68 2, 273-287, 2008. · Zbl 1132.46002 · doi:10.1016/j.na.2006.10.047 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.