Some mapping properties of \(p\)-summing adjoint operators
type: Item
instance of: scholarly article
title: Some mapping properties of \(p\)-summing adjoint operators
zbMATH Open document ID: 1071.47025
author: Qingying Bu
author: Przemo T. Kranz
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-07T00:00:00Z
review text: A sequence \(x_n\) in a Banach space \(X\) is called almost unconditionally summable if the series \(\sum \pm x_n\) converge for almost all choices of signs \(\pm\). Let \(X, Y\) be Banach spaces, \(u:X \to Y\) be a continuous linear operator. If \(u^*: Y^* \to X^*\) is \(p\)-summing for some \(p \geq 1\), then for any \(q \geq 2\), \(u\) takes almost unconditionally summable sequences in \(X\) into elements of \(l_q \widehat{\otimes} Y\), the projective product of \(l_q\) and \(Y\). Moreover, if \(X\) has type 2, then \(u\) takes almost unconditionally summable sequences in \(X\) into elements of \(l_2 \widehat{\otimes} Y\) if and only if \(u^*\) is 2-summing.
reviewed by: Vladimir Kadets
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 2153767
zbMATH Keywords: almost unconditionally summable sequence
zbMATH Keywords: projective tensor product
zbMATH Keywords: \(p\)-summing operator
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.08.054
OpenAlex ID: W1994379587
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DOI: 10.1016/J.JMAA.2004.08.054
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description: scientific article; zbMATH DE number 2153767