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 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. © 2010 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
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Citas:
---------- APA ----------
Carando, D. & Galicer, D.
(2010)
. Extending polynomials in maximal and minimal ideals. Publications of the Research Institute for Mathematical Sciences, 46(3), 669-680.
http://dx.doi.org/10.2977/PRIMS/21---------- CHICAGO ----------
Carando, D., Galicer, D.
"Extending polynomials in maximal and minimal ideals"
. Publications of the Research Institute for Mathematical Sciences 46, no. 3
(2010) : 669-680.
http://dx.doi.org/10.2977/PRIMS/21---------- MLA ----------
Carando, D., Galicer, D.
"Extending polynomials in maximal and minimal ideals"
. Publications of the Research Institute for Mathematical Sciences, vol. 46, no. 3, 2010, pp. 669-680.
http://dx.doi.org/10.2977/PRIMS/21---------- VANCOUVER ----------
Carando, D., Galicer, D. Extending polynomials in maximal and minimal ideals. Publ. Res. Inst. Math. Sci. 2010;46(3):669-680.
http://dx.doi.org/10.2977/PRIMS/21