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
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页码：669 / 680
页数：12
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