Extension of vector-valued integral polynomials
We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral po...
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| Autores principales: | , |
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| Formato: | Artículo publishedVersion |
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2005
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v307_n1_p77_Carando https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v307_n1_p77_Carando_oai |
| Aporte de: |
| Sumario: | We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they are extendible to X-valued polynomials. The Aron-Berner extension of an integral polynomial is also studied. A canonical integral representation is given for domains not containing ℓ1. © 2004 Elsevier Inc. All rights reserved. |
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