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–Berner 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.
Cite this article
Daniel Carando, Daniel Galicer, Extending Polynomials in Maximal and Minimal Ideals. Publ. Res. Inst. Math. Sci. 46 (2010), no. 3, pp. 669–680DOI 10.2977/PRIMS/21