This is an announcement for the paper "Extending polynomials in maximal and minimal ideals" by Daniel Carando and Daniel Galicer.

Abstract: 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.

Archive classification: math.FA

Mathematics Subject Classification: 46G25; 46A32; 46B28; 47H60

Remarks: 10 pages

The source file(s), ExtendingCarandoGalicer.tex: 34351 bytes, is(are) stored in gzipped form as 0910.3888.gz with size 11kb. The corresponding postcript file has gzipped size 93kb.

Submitted from: dgalicer@dm.uba.ar

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0910.3888

or

http://arXiv.org/abs/0910.3888

or by email in unzipped form by transmitting an empty message with subject line

uget 0910.3888

or in gzipped form by using subject line

get 0910.3888

to: math@arXiv.org.