Extending Polynomials in Maximal and Minimal Ideals

被引：8

作者：

Carando, Daniel ^{[1
,2
]}

Galicer, Daniel ^{[1
,2
]}

机构：

[1] Univ Buenos Aires, Fac Cs Exactas & Nat, Dept Matemat Pab 1, RA-1428 Buenos Aires, DF, Argentina

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

来源：

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES | 2010年 / 46卷 / 03期

关键词：

extension of polynomials; polynomial ideals; symmetric tensor products of Banach spaces; BANACH-SPACES; ANALYTIC-FUNCTIONS; MULTILINEAR MAPPINGS; EXTENSION THEOREM; HOLOMORPHY TYPES; ULTRAPRODUCTS;

D O I：

10.2977/PRIMS/21

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a homogeneous polynomial on a Banach space E belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of E and prove that this extension remains in the ideal and has the same ideal norm As a consequence, we show that the Aron-Bernei extension is a well defined isometry for any maximal or minimal ideal of homogeneous polynomials This allows us to obtain symmetric versions of some basic results of the metric theory of tensor products

引用

页码：669 / 680

页数：12

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