On multilinear generalizations of the concept of nuclear operators

Dahmane Achour ¹   ; Ahlem Alouani ²

¹ Department of Mathematics M'sila University 28000 M'sila, Algeria
² Department of Mathematics Tebessa University 12000 Tebessa, Algeria

Colloquium Mathematicum, Tome 120 (2010) no. 1, pp. 85-102

Résumé

This paper introduces the class of Cohen $p$-nuclear $m$-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing $m$-linear operators are established. As a consequence of our results, we show that every Cohen $p$-nuclear ($1 p\le \infty $) $m$-linear mapping on arbitrary Banach spaces is weakly compact.

Détail

DOI : 10.4064/cm120-1-7

Keywords: paper introduces class cohen p nuclear m linear operators between banach spaces characterization terms pietschs domination theorem proved interpretation terms factorization gives factorization theorem similar kwapie factorization theorem dominated linear operators connections theory absolutely summing m linear operators established consequence results every cohen p nuclear infty m linear mapping arbitrary banach spaces weakly compact