JournalsprimsVol. 46, No. 3pp. 669–680

Extending Polynomials in Maximal and Minimal Ideals

  • Daniel Carando

    Universidad de Buenos Aires, Argentina
  • Daniel Galicer

    Universidad de Buenos Aires, Argentina
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Abstract

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 defi ned 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. 669–680

DOI 10.2977/PRIMS/21