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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 100, Issue 1
  • July 1986, pp. 161-166

Sequence spaces defined by a modulus

  • I. J. Maddox (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100065968
  • Published online: 24 October 2008
Abstract

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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[4]W. H. Ruckle . FK spaces in which the sequence of coordinate vectors is bounded. Canad. J. Math. 25 (1973), 973978.

[5]B. Thorpe . An extension of Kuttner's theorem. Bull. London Math. Soc. 13 (1981), 301302.

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