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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 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.

Registro:

Documento: Artículo
Título:Extending polynomials in maximal and minimal ideals
Autor:Carando, D.; Galicer, D.
Filiación:Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
CONICET, Argentina
Palabras clave:Extension of polynomials; Polynomial ideals; Symmetric tensor products of banach spaces
Año:2010
Volumen:46
Número:3
Página de inicio:669
Página de fin:680
DOI: http://dx.doi.org/10.2977/PRIMS/21
Título revista:Publications of the Research Institute for Mathematical Sciences
Título revista abreviado:Publ. Res. Inst. Math. Sci.
ISSN:00345318
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00345318_v46_n3_p669_Carando.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00345318_v46_n3_p669_Carando

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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