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

S0305004100065968_eqn1

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)