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On the inclusion of a bounded convergence field in the space of almost convergent sequences

Published online by Cambridge University Press:  18 May 2009

Robert E. Atalla
Robert E. Atalla
Affiliation:
Ohio University, Athens, Ohio
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Let T = (tmn) be a regular matrix, and CTbe its bounded convergence field. Necessary and sufficient conditions for CT to contain the space of almost convergent sequences are well known. (See, e.g., [7, p.62]). G. M. Petersen has suggested as a problem for research the discovery of necessary and sufficient conditions for the reverse inclusion: When is CT contained in the space of almost convergent sequences? [7, p. 137, research problem 9]. In this paper we deal with this question in a more general context. First we need some notation.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 1 , March 1972 , pp. 82 - 90
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Atalla, R., On the multiplicative behavior of regular matrices; to appear.Google Scholar
2.Atalla, R. and Bustoz, J., Sequential cores and a theorem of R. R. Phelps, Proc. Amer. Math. Soc. 21 (1969), 36–42.CrossRefGoogle Scholar
3.Day, M. M., Normed linear spaces (New York, 1962).CrossRefGoogle Scholar
4.Dean, D. and Raimi, R. A., Permutations with comparable sets of invariant means, Duke Math. J. 27 (1960), 467–480.CrossRefGoogle Scholar
5.Dunford, N. and Schwartz, J., Linear operators, Vol.I (New York, 1958).Google Scholar
6.Jerison, M., A property of extreme points of compact convex sets, Proc. Amer. Math. Soc. 5 (1954), 782–783.CrossRefGoogle Scholar
7.Petersen, G. M., Regular matrix transformations(MCGraw-Hill, London, 1966).Google Scholar
8.Raimi, R. A., Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963), 81–94.CrossRefGoogle Scholar