On multilinear generalizations of the concept of nuclear operators

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 -