Coincidence of extendible vector-valued ideals with their minimal kernel

被引：6
|
作者：
Galicer, Daniel [1 ,2 ]
Villafane, Roman [1 ,2 ]
机构：
[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
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 421卷 / 02期
关键词：
Multilinear mappings; Radon-Nikodym property; Polynomial ideals; Metric theory of tensor products; HOMOGENEOUS POLYNOMIALS; MULTILINEAR MAPPINGS; TENSOR-PRODUCTS; BANACH; SPACES; APPROXIMATION; NUCLEAR; BASES;
D O I：
10.1016/j.jmaa.2014.07.023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：1743 / 1766
页数：24
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