Coincidence of extendible vector-valued ideals with their minimal kernel

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:421

Article

Galicer, Daniel^1,2  Villafane, Roman^1,2 

[1] Univ Buenos Aires, Fac Cs Exactas & Nat, Dept Matemat Pab 1, Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, IMAS, RA-1033 Buenos Aires, DF, Argentina

关键词: Multilinear mappings;    Radon-Nikodym property;    Polynomial ideals;    Metric theory of tensor products;   

DOI  :  10.1016/j.jmaa.2014.07.023

来源: Elsevier

【 摘 要 】

We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if U is an ideal of n-linear mappings we give conditions for which the equality U(E-1, . . . , E-n; F) = U-min(E-1, . . . , E-n ; F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space U(E-1, . . . , E-n; F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where U is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials. (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free