Móricz, F. Extensions of the spaces \(c\) and \(c_ 0\) from single to double sequences. (English) Zbl 0781.46025 Acta Math. Hung. 57, No. 1-2, 129-136 (1991). The author has taken up the study of some sub-spaces of double sequences of complex numbers under both the regular convergence as well as the convergence in Pringsheim’s sense. He shows that the space of regularly convergent sequences is complete under the sup norm and the space of sequences convergent in Psingsheim’s sense is complete under an associated pseudonorm. He has also given some representation theorem for bounded linear functionals on these spaces. Reviewer: G.D.Dikshit (Auckland) Cited in 72 Documents MSC: 46B45 Banach sequence spaces 46A45 Sequence spaces (including Köthe sequence spaces) 46B25 Classical Banach spaces in the general theory 40B05 Multiple sequences and series Keywords:sub-spaces of double sequences of complex numbers; regular convergence; convergence in Pringsheim’s sense PDFBibTeX XMLCite \textit{F. Móricz}, Acta Math. Hung. 57, No. 1--2, 129--136 (1991; Zbl 0781.46025) Full Text: DOI References: [1] G. H. Hardy, On the convergence of certain multiple series,Proc. Cambridge Philos. Soc.,19 (1916–1919), 86–95. · JFM 46.0405.01 [2] F. Móricz, Some remarks on the notion of regular convergence of multiple series,Acta. Math. Hungar.,41 (1983), 161–168. · Zbl 0525.40002 [3] W. Rudin,Functional Analysis, McGraw-Hill, Inc. (New York, 1973). · Zbl 0253.46001 [4] K. Yosida,Functional Analysis, Academic Press, Springer (Berlin-Göttingen-Heidelberg, 1965). · Zbl 0126.11504 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.