Abstract

In this not we consider several types of gliding bump properties for a sequence space E and we consider the various implications between these properties. By means of examples we show that most of the implications are strict and they afford a sort of structure between solid sequence spaces and those with weakly sequentially complete β-duals. Our main result is used to extend a result of Bennett and Kalton which characterizes the class of sequence spaces E with the properly that E⊂SF, whenever F is a separable FK space containing E where SF denotes the sequences in F having sectional convergence. This, in turn, is used to identify a gliding humps property as a sufficient condition for E to be in this class.