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Sequence spaces defined by a modulus

  • I. J. Maddox (a1)
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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?’

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References
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[1]Kuttner, B.. Note on strong summability. J. London Math. Soc. 21 (1946), 118122.
[2]Maddox, I. J.. On Kuttner's theorem. J. London Math. Soc. 43 (1968), 285290.
[3]Maddox, I. J.. Series in locally convex spaces and inclusions between FK spaces. Math. Proc. Cambridge Philos. Soc. 95 (1984), 467472.
[4]Ruckle, W. H.. FK spaces in which the sequence of coordinate vectors is bounded. Canad. J. Math. 25 (1973), 973978.
[5]Thorpe, B.. An extension of Kuttner's theorem. Bull. London Math. Soc. 13 (1981), 301302.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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