Sequence spaces defined by a modulus

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 { e 1 , e 2 , …} of unit vectors is bounded?’