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A characterization of a class of barrelled sequence spaces

Published online by Cambridge University Press:  18 May 2009

J. Swetits
J. Swetits
Affiliation:
Department of Mathematical and Computing Sciences, Old Dominion University, Norfolk, Virginia 23508
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In a recent paper [4] Bennett and Kalton characterized dense, barrelled subspaces of an arbitrary FK space, E. In this note, it is shown that if E is assumed to be an AK space, then the characterization assumes a simpler and more explicit form.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 1 , January 1978 , pp. 27 - 31
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

1.Bennett, G., A representation theorem for summability domains, Proc. London Math. Soc 24 (1972), 193–203.CrossRefGoogle Scholar
2.Bennett, G., Some inclusion theorems for sequence spaces, Pacific J. Math. 46 (1973), 17–30.CrossRefGoogle Scholar
3.Bennett, G., A new class of sequence spaces with applications in summability theory, J. Reine Angew. Math. 266 (1974), 49–75.Google Scholar
4.Bennett, G. and Kalton, N. J., Inclusion theorems for K spaces, Canad. J. Math. 25 (1973), 511–524.CrossRefGoogle Scholar
5.Bennett, G. and Kalton, N. J., Consistency theorems for almost convergence, Trans. Amer. Math. Soc. 198 (1974), 23–43.CrossRefGoogle Scholar
6.Lorentz, G. G., A contribution to the theory of divergent sequences, Ada. Math. 80 (1948), 167–190.Google Scholar
7.Robertson, A. P. and Robertson, W. J., Topological vector spaces, (Cambridge, 1963).Google Scholar
8.Swetits, J., On the relationship between a summability matrix and its transpose, Old Dominion University, Department of Mathematical and Computing Sciences Technical Report, TR-76–2, (1976).Google Scholar
9.Wilansky, A., Functional analysis (Blaisdell, New York, 1964).Google Scholar
10.Garling, D. J. H., The β and γ duality of sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967), 963–981.CrossRefGoogle Scholar