Gliding hump properties and some applications
type: Item
instance of: scholarly article
title: Gliding hump properties and some applications
zbMATH Open document ID: 0824.46007
DOI: 10.1155/S0161171295000160
author: Daniel J. Fleming
author: Johann Boos
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1995-10-26T00:00:00Z
full work available at URL: https://eudml.org/doc/47280
review text: 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.
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A35
Mathematics Subject Classification ID: 40D25
Mathematics Subject Classification ID: 40H05
zbMATH DE Number: 733304
zbMATH Keywords: sectional convergence in FK spaces
zbMATH Keywords: theorem of Schur
zbMATH Keywords: theorem of Hahn
zbMATH Keywords: gliding hump properties
zbMATH Keywords: sequence space
zbMATH Keywords: weakly sequentially complete \(\beta\)-duals
zbMATH Keywords: separable FK space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 733304