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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.
Dahmane Achour, and Ahlem Alouani. "On multilinear generalizations of the concept of nuclear operators." Colloquium Mathematicae 120.1 (2010): 85-102. <http://eudml.org/doc/283525>.
@article{DahmaneAchour2010, abstract = {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.}, author = {Dahmane Achour, Ahlem Alouani}, journal = {Colloquium Mathematicae}, keywords = {-nuclear operators; Pietsch's domination theorem; factorisation theorem; absolutely summing operators}, language = {eng}, number = {1}, pages = {85-102}, title = {On multilinear generalizations of the concept of nuclear operators}, url = {http://eudml.org/doc/283525}, volume = {120}, year = {2010}, }
TY - JOUR AU - Dahmane Achour AU - Ahlem Alouani TI - On multilinear generalizations of the concept of nuclear operators JO - Colloquium Mathematicae PY - 2010 VL - 120 IS - 1 SP - 85 EP - 102 AB - 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. LA - eng KW - -nuclear operators; Pietsch's domination theorem; factorisation theorem; absolutely summing operators UR - http://eudml.org/doc/283525 ER -