Weak sequential completeness of sequence spaces
type: Item
instance of: scholarly article
title: Weak sequential completeness of sequence spaces
zbMATH Open document ID: 0782.46013
published in: Collectanea Mathematica
publication date: 1994-03-10T00:00:00Z
full work available at URL: https://eudml.org/doc/41848
review text: It is shown that a classical theorem of summability due to Schur and Hahn can be used to give a straightforward proof of a theorem of Bennett and Kalton which asserts that the \(\beta\)-dual of a monotone sequence space is weakly sequentially complete. The methods also work for vector-valued sequence spaces. Applications to Hellinger-Toeplitz Theorems are given.
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46B45
zbMATH DE Number: 425614
zbMATH Keywords: theorem of Bennett and Kalton
zbMATH Keywords: \(\beta\)-dual of a monotone sequence space is weakly sequentially complete
zbMATH Keywords: vector-valued sequence spaces
zbMATH Keywords: Hellinger-Toeplitz Theorems
author: Charles Swartz
reviewed by: Charles Swartz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 425614