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Sequence spaces defined by a modulus

Published online by Cambridge University Press:  24 October 2008

I. J. Maddox
I. J. Maddox
Affiliation:
The Queen's University of Belfast
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Extract

Ruckle[4] used the idea of a modulus function ƒ (see Definition 1 below) to construct the sequence space

This space is an FK space, and Ruckle proved that the intersection of all such L(f) spaces is ø, the space of finite sequences, thereby answering negatively a question of A. Wilansky: ‘Is there a smallest FK-space in which the set {e1, e2, …} of unit vectors is bounded?’

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 1 , July 1986 , pp. 161 - 166
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Kuttner, B.. Note on strong summability. J. London Math. Soc. 21 (1946), 118–122.Google Scholar
[2]Maddox, I. J.. On Kuttner's theorem. J. London Math. Soc. 43 (1968), 285–290.CrossRefGoogle Scholar
[3]Maddox, I. J.. Series in locally convex spaces and inclusions between FK spaces. Math. Proc. Cambridge Philos. Soc. 95 (1984), 467–472.CrossRefGoogle Scholar
[4]Ruckle, W. H.. FK spaces in which the sequence of coordinate vectors is bounded. Canad. J. Math. 25 (1973), 973–978.CrossRefGoogle Scholar
[5]Thorpe, B.. An extension of Kuttner's theorem. Bull. London Math. Soc. 13 (1981), 301–302.CrossRefGoogle Scholar