On multilinear generalizations of the concept of nuclear operators
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.