The ideal of p-compact operators: a tensor product approach

Daniel Galicer ; Silvia Lassalle ; Pablo Turco

Studia Mathematica, Tome 209 (2012), p. 269-286 / Harvested from The Polish Digital Mathematics Library

Résumé

We study the space of p-compact operators, $_{p}$, using the theory of tensor norms and operator ideals. We prove that $_{p}$ is associated to $/d_{p}$, the left injective associate of the Chevet-Saphar tensor norm $d_{p}$ (which is equal to $g_{p^{\prime }}^{\prime }$). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that $_{p}(E;F)$ is equal to $_{q}(E;F)$ for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of $_{p}$. For instance, we show that $_{p}$ is regular, surjective, and totally accessible, and we characterize its maximal hull $_{p}^{max}$ as the dual ideal of p-summing operators, $Π_{p}^{dual}$. Furthermore, we prove that $_{p}$ coincides isometrically with $_{p}^{dual}$, the dual to the ideal of the quasi p-nuclear operators.

Détail

Publié le : 2012-01-01

Zbl 1269.47052

EUDML-ID : urn:eudml:doc:285912