Gliding hump properties and some applications
Summary: We consider several types of gliding hump 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 \(\beta\)-duals. Our main result is used to extend a result of Bennett and Kalton which characterizes the class of sequence spaces \(E\) with the property that \(E\subset S_ F\) whenever \(F\) is a separable FK space containing \(E\) where \(S_ F\) denotes the sequences in \(F\) having sectional convergence. This, in turn, is used to identify a gliding hump property as a sufficient condition for \(E\) to be in this class.
weakly sequentially complete \(\beta\)-duals
scientific article; zbMATH DE number 733304