On multilinear generalizations of the concept of nuclear operators

• Autorzy: Dahmane Achour , Ahlem Alouani
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L22: Ideals of polynomials and of multilinear mappings
• 46G25: (Spaces of) multilinear mappings, polynomials
• 46B25: Classical Banach spaces in the general theory
• 47H60: Multilinear and polynomial operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 120
• Numer: 1
• Strony: 85-102

Daty

wydano

2010

Twórcy

autor

Dahmane Achour

• Department of Mathematics, M'sila University, 28000 M'sila, Algeria

autor

Ahlem Alouani

• Department of Mathematics, Tebessa University, 12000 Tebessa, Algeria

Identyfikatory

DOI

10.4064/cm120-1-7