Extending polynomials in maximal and minimal ideals

Details Extending polynomials in maximal and minimal ideals Extending polynomials in maximal and minimal ideals

2009-10-20

arxiv.org/abs/0910.3888v2

Publ. RIMS Kyoto Univ. 46 (2010), 669-680

Mathematics

Functional Analysis

13 pages

Scientific paper

10.2977/PRIMS/21

Given an 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-Berner extension is a well defined isometry for any maximal or minimal ideal of homogeneous polynomials. This allow us to obtain symmetric versions of some basic results of the metric theory of tensor products.

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