On multilinear generalizations of the concept of nuclear operators

Dahmane Achour; Ahlem Alouani

Colloquium Mathematicae (2010)

  • Volume: 120, Issue: 1, page 85-102
  • ISSN: 0010-1354

Abstract

top
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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.