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Zbl 0781.46025
Móricz, F.
Extensions of the spaces $c$ and $c\sb 0$ from single to double sequences. (English)
[J] Acta Math. Hung. 57, No.1-2, 129-136 (1991). ISSN 0236-5294; ISSN 1588-2632/e

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.
[G.D.Dikshit (Auckland)]

MSC 2000:: *46B45 Banach sequence spaces
46A45 Sequence spaces
46B25 Classical Banach spaces in the general theory of normed spaces
40B05 Multiple sequences and series

Keywords: sub-spaces of double sequences of complex numbers; regular convergence; convergence in Pringsheim's sense

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