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On multilinear generalizations of the concept of nuclear operators

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Achour D., Alouani A.

Colloquium Mathematicum

2010

tom 120

nr 1

85-102

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Achour D.

1 Alouani A.

1 2010

Wyniki wyszukiwania

On multilinear generalizations of the concept of nuclear operators