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Preduals and Nuclear Operators Associated with Bounded, $p$-Convex, $p$-Concave and Positive $p$-Summing Operators

Published online by Cambridge University Press:  20 November 2018

C. C. A. Labuschagne
C. C. A. Labuschagne*
Affiliation:
School of Mathematics, University of the Witwatersrand, South Africa email: Coenraad.Labuschagne@wits.ac.za, cola@maths.wits.ac.za
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Abstract

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We use Krivine's form of the Grothendieck inequality to renorm the space of bounded linear maps acting between Banach lattices. We construct preduals and describe the nuclear operators associated with these preduals for this renormed space of bounded operators as well as for the spaces of $p$-convex, $p$-concave and positive $p$-summing operators acting between Banach lattices and Banach spaces. The nuclear operators obtained are described in terms of factorizations through classical Banach spaces via positive operators.

Keywords

46B2847B1046B4246B45p-convex operatorp-concave operatorp-summing operatorBanach spaceBanach latticenuclear operatorsequence space
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 3 , 01 June 2007 , pp. 614 - 637
Copyright
Copyright © Canadian Mathematical Society 2007

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