Absolutely \(p\)-summable sequences in Banach spaces and range of vector measures
type: Item
instance of: scholarly article
title: Absolutely \(p\)-summable sequences in Banach spaces and range of vector measures
zbMATH Open document ID: 1172.46028
DOI: 10.1216/RMJ-2008-38-3-993
published in: Rocky Mountain Journal of Mathematics
publication date: 2009-04-07T00:00:00Z
review text: The author studies the question, given \(1 \leq p<\infty\), for what Banach spaces \(X\) every \(p\)-summable sequence of elements of \(X\) (i.e., a sequence \((x_i)\) in \(X\) with \(\sum_i \|x_i\|^p < \infty\)) is contained in the range of some \(X\)-valued measure. Most of the results establish necessary and sufficient conditions on \(X\) to have properties of such kind in terms of \((p,q)\)-absolutely summing operators from \(X\) to \(\ell_1\). Besides, some examples and open problems are given.
reviewed by: M. M. Popov
Mathematics Subject Classification ID: 46G10
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 5541254
zbMATH Keywords: vector measure
zbMATH Keywords: \(p\)-summing maps
zbMATH Keywords: absolutely \(p\)-summing sequences
author: Mohd Amin Sofi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5541254