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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2001.tde-20220712-115450
Document
Author
Full name
Leonardo Pellegrini Rodrigues
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2001
Supervisor
Title in Portuguese
Um teorema de Hahn-Banach para polinômios homogêneos
Keywords in Portuguese
Holomorfia
Polinômios
Abstract in Portuguese
O objetivo deste trabalho é estudar um teorema de Hahn-Banach para polinômios homogêneos. Apresentamos aqui uma prova, dada por Davie e Gamelin em [7], de que existe uma extensão que preserva a norma de polinômios homogêneos para o bidual. Mostramos também que há uma única extensão que preserva a norma para polinômios 2-homogêneos que atingem a norma em 'c.IND. 0' para 'l.INFINITO', mas não há uma única extensão que preserva a norma 'P(POT. n l.INFINITO'), para n>2. Estudamos também extensões que preservam a norma para polinômios nucleares de um M-ideal para seu bidual. Os resultados acima foram obtidos por Aron, Boyd e Choi em [2]
Title in English
not available
Abstract in English
The main purpose of this work is to study a Hahn-Banach theorem for homogeneous polynomials. We present here a proof, given by Davie e Gamelin in [7], that there is a norm-preserving extension for homogeneous polynomials to the bidual. We also show that there is a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on 'c.IND. 0' to 'l.INFINITO, but there is no unique norm-preserving extension for 'P(POT. n c.IND. 0)' to 'P(POT. n l.INFINITO), for n>2. We study norm-preserving extension of nuclear polynomials from an M-ideal to its bidual. The results above were obtained by Aron, Boyd e Choi in [2]
 
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Publishing Date
2022-07-13
 
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