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

Labuschagne, C. C. A.

Canadian journal of mathematics, Tome 59 (2007) no. 3, pp. 614-637

Résumé

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.

Détail

DOI : 10.4153/CJM-2007-026-2

Mots-clés : 46B28, 47B10, 46B42, 46B45, p-convex operator, p-concave operator, p-summing operator, Banach space, Banach lattice, nuclear operator, sequence space

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