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 ≤ ∞ ) m-linear mapping on arbitrary Banach spaces is weakly compact.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-7,
author = {Dahmane Achour and Ahlem Alouani},
title = {On multilinear generalizations of the concept of nuclear operators},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {85-102},
zbl = {1219.47095},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-7}
}
Dahmane Achour; Ahlem Alouani. On multilinear generalizations of the concept of nuclear operators. Colloquium Mathematicae, Tome 120 (2010) pp. 85-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-7/