Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Sequence spaces defined by a modulus

I. J. Maddoxa1

a1 The Queen's University of Belfast

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?’

(Received August 23 1985)