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## On multilinear generalizations of the concept of nuclear operators

### Tom 120 / 2010

Colloquium Mathematicum 120 (2010), 85-102 MSC: 47H60, 46G25, 46B25, 47L22. DOI: 10.4064/cm120-1-7

#### Streszczenie

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.

#### Autorzy

• Dahmane AchourDepartment of Mathematics
M'sila University
28000 M'sila, Algeria
e-mail
• Ahlem AlouaniDepartment of Mathematics
Tebessa University
12000 Tebessa, Algeria
e-mail

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