On Rosenthal's \(\ell^ 1\)-theorem
type: Item
instance of: scholarly article
title: On Rosenthal's \(\ell^ 1\)-theorem
zbMATH Open document ID: 0794.46016
DOI: 10.1007/BF01201788
author: Ehrhard Behrends
published in: Archiv der Mathematik
publication date: 1994-05-09T00:00:00Z
review text: Rosenthal's \(\ell^ 1\)-theorem can be restated by saying that a bounded sequence \((x_ n)\) in a Banach space admits a subsequence which is weakly Cauchy provided that there are ``many'' arbitrarily small \(\ell^ 1\)-blocks of the \(x_ n\). Here we show that there is even a norm convergent subsequence if these blocks can be chosen such that their length is bounded.
reviewed by: Ehrhard Behrends
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 566518
zbMATH Keywords: Rosenthal's \(\ell^ 1\)-theorem
zbMATH Keywords: small \(\ell^ 1\)-blocks
MaRDI profile type: Publication
cites work: On bases and unconditional convergence of series in Banach spaces
cites work: Q3329946
cites work: A Characterization of Banach Spaces Containing l 1
description: scientific article; zbMATH DE number 566518