International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 121-132
doi:10.1155/S0161171295000160

Gliding hump properties and some applications

Johann Boos1 and Daniel J. Fleming2

1Fachbereich Mathematik, FernUniversität Gesamthochschule, Hagen D 58084, Germany
2Department of Mathematics, St. Lawrence Univesity, Canton 13617, NY, USA

Received 21 July 1993

Copyright © 1995 Johann Boos and Daniel J. Fleming. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.