Extending polynomials in maximal and minimal ideals
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...
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| Autores principales: | , |
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| Formato: | Artículo publishedVersion |
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2010
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00345318_v46_n3_p669_Carando http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00345318_v46_n3_p669_Carando_oai |
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| Sumario: | 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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